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## Fairweather, Graeme

Compute Distance To:
 Author ID: fairweather.graeme Published as: Fairweather, G.; Fairweather, Graeme
 Documents Indexed: 120 Publications since 1964, including 5 Books
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#### Co-Authors

 12 single-authored 20 Bialecki, Bernard 18 Karageorghis, Andreas 9 Keast, Patrick 7 Mitchell, Andrew Ronald 7 Pani, Amiya Kumar 6 Fernandes, Ryan I. 5 Diaz, Julio Cesar 5 López-Marcos, Juan Carlos 4 Gladwell, Ian 4 Johnston, Roy L. 4 Nguyen, Que N. 4 Sun, Weiwei 3 Bennett, Karin R. 3 Dendy, Joel E. jun. 3 Gourlay, A. R. 3 Johnson, J. Peter 3 Li, Bingkun 3 Robinson, Mark P. 3 Shippy, David J. 2 Bhal, Santosh Kumar 2 Danumjaya, Palla 2 Du, Kui 2 Khebchareon, Morrakot 2 Kondapalli, Prasanna S. 2 Majaess, Fouad 2 Martin, Paul Andrew 2 Micula, Gheorghe 2 Saylor, Annie V. 2 Seward, Wendy L. 2 Smyrlis, Yiorgos-Sokratis 2 Tankelevich, Roman 2 Xu, Da 2 Yang, Xuehua 2 Yanik, Elizabeth Greenwell 2 Zhang, Haixiang 1 Amodio, Pierluigi 1 Cai, Xiao-Chuan 1 Cash, Jeff R. 1 Christie, Ian 1 Dryja, Maksymilian 1 Dupont, Todd F. 1 Greenwell-Yanik, C. E. 1 Herbst, Ben M. 1 Karageorhis, A. 1 Kasibhatla, Prasad S. 1 Knudson, David B. 1 Kraut, G. L. 1 Leimkuhler, Benedict J. 1 Li, Zhi 1 Lin, Qun 1 Lin, Yanping 1 Lipman, D. Abram 1 Lou, Zhou-Ming 1 Ma, Heping 1 Maack, Jon 1 Maack, Jonathan 1 Maede, Daniel 1 Muir, Paul H. 1 Navon, Ionel Michael 1 Paprzycki, Marcin 1 Pew, Jack 1 Remington, Karin A. 1 Rizzo, Frank J. 1 Roussos, Giannis 1 Rudolphi, Thomas J. 1 Sanz-Serna, Jesús María 1 Saylor, Rick D. 1 Sloan, Ian Hugh 1 Tannahill, Connor 1 Tran, Dat Hoang 1 Tripathi, Lok Pati 1 Van Vleck, Erik S. 1 Vedha-Nayagam, M. 1 Wang, Junping 1 Weinberg, Gadalia M. 1 Wright, R. W. 1 Wu, Yensen S. 1 Yan, Yi 1 Zhang, Shuhua
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#### Serials

 16 SIAM Journal on Numerical Analysis 7 IMA Journal of Numerical Analysis 7 Journal of Computational Physics 6 Mathematics of Computation 5 ACM Transactions on Mathematical Software 5 Numerische Mathematik 4 Journal of Computational and Applied Mathematics 3 International Journal for Numerical Methods in Engineering 3 Applied Numerical Mathematics 3 Numerical Methods for Partial Differential Equations 3 Journal of Scientific Computing 3 Numerical Algorithms 3 SIAM Journal on Scientific Computing 3 Advances in Computational Mathematics 3 Engineering Analysis with Boundary Elements 2 Computers & Mathematics with Applications 2 Journal of the Institute of Mathematics and its Applications 2 BIT 2 The Computer Journal. Section A / Section B 2 SIAM Review 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Scientific and Statistical Computing 1 Numerical Heat Transfer 1 Communications in Applied Numerical Methods 1 Computational Mechanics 1 Mathematical and Computer Modelling 1 Applied Mathematical Modelling 1 Studia Universitatis Babeş-Bolyai. Mathematica 1 Revue d’Analyse Numérique et de Théorie de l’Approximation 1 Numerical Linear Algebra with Applications 1 East-West Journal of Numerical Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Journal of Computational Acoustics 1 Journal of the Society for Industrial & Applied Mathematics 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Lecture Notes in Pure and Applied Mathematics 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 Advances in Applied Mathematics and Mechanics 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 100 Numerical analysis (65-XX) 54 Partial differential equations (35-XX) 15 Integral equations (45-XX) 11 Ordinary differential equations (34-XX) 11 Fluid mechanics (76-XX) 8 Mechanics of deformable solids (74-XX) 5 Potential theory (31-XX) 4 Approximations and expansions (41-XX) 3 General and overarching topics; collections (00-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH

98 Publications have been cited 1,948 times in 1,223 Documents Cited by Year
The method of fundamental solutions for elliptic boundary value problems. Zbl 0922.65074
Fairweather, Graeme; Karageorghis, Andreas
1998
The method of fundamental solutions for scattering and radiation problems. Zbl 1060.76649
Fairweather, Graeme; Karageorghis, Andreas; Martin, P. A.
2003
The method of fundamental solutions for the numerical solution of the biharmonic equation. Zbl 0618.65108
Karageorghis, Andreas; Fairweather, Graeme
1987
Finite element methods for parabolic and hyperbolic partial integro- differential equations. Zbl 0657.65142
Yanik, Elizabeth G.; Fairweather, Graeme
1988
Finite element Galerkin methods for differential equations. Zbl 0372.65044
Fairweather, Graeme
1978
Orthogonal spline collocation methods for partial differential equations. Zbl 0971.65105
Bialecki, B.; Fairweather, G.
2001
$$H^1$$-Galerkin mixed finite element methods for parabolic partial integro-differential equations. Zbl 1008.65101
Pani, Amiya K.; Fairweather, Graeme
2002
A new computational procedure for A.D.I. methods. Zbl 0252.65072
Fairweather, G.; Mitchell, A. R.
1967
FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. Zbl 0516.65013
Diaz, J. C.; Fairweather, G.; Keast, P.
1983
The method of fundamental solutions for problems in potential flow. Zbl 0546.76021
Johnston, R. L.; Fairweather, G.
1984
Orthogonal spline collocation methods for Schrödinger-type equations in one space variable. Zbl 0806.65123
Robinson, Mark P.; Fairweather, Graeme
1994
The reformulation and numerical solution of certain nonclassical initial- boundary value problems. Zbl 0722.65062
Fairweather, Graeme; Saylor, Rick D.
1991
Three-level Galerkin methods for parabolic equations. Zbl 0313.65107
Dupont, Todd; Fairweather, Graeme; Johnson, J. Peter
1974
The method of fundamental solutions for axisymmetric elasticity problems. Zbl 1011.74005
Karageorghis, A.; Fairweather, G.
2000
Orthogonal spline collocation methods for some partial integrodifferential equations. Zbl 0756.65157
Yan, Yi; Fairweather, Graeme
1992
The method of fundamental solutions for axisymmetric potential problems. Zbl 0932.74078
Karageorghis, Andreas; Fairweather, Graeme
1999
Matrix decomposition algorithms for elliptic boundary value problems: A survey. Zbl 1208.65036
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas
2011
Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Zbl 0868.65068
Fairweather, G.; López-Marcos, J. C.
1996
Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0595.65122
Greenwell-Yanik, C. E.; Fairweather, G.
1986
Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations. Zbl 0123.12001
Mitchell, A. R.; Fairweather, G.
1964
Spline collocation methods for a class of hyperbolic partial integro- differential equations. Zbl 0814.65137
Fairweather, Graeme
1994
ADI orthogonal spline collocation methods for parabolic partial integro-differential equations. Zbl 1191.65186
Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I.
2010
Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term. Zbl 1160.65068
Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I.
2008
Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations. Zbl 0752.65076
Bialecki, Bernard; Fairweather, Graeme; Bennett, Karin R.
1992
The simple layer potential method of fundamental solutions for certain biharmonic problems. Zbl 0687.76028
Karageorghis, Andreas; Fairweather, Graeme
1989
The method of fundamental solutions for the solution of nonlinear plane potential problems. Zbl 0676.65110
Karageorghis, A.; Fairweather, G.
1989
The Almansi method of fundamental solutions for solving biharmonic problems. Zbl 0639.65066
Karageorghis, Andreas; Fairweather, Graeme
1988
Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. Zbl 0911.65095
Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
1998
An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation. Zbl 1328.65216
Fairweather, Graeme; Yang, Xuehua; Xu, Da; Zhang, Haixiang
2015
Algorithms for almost block diagonal linear systems. Zbl 1062.65031
2004
Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. Zbl 0781.65031
Bialecki, Bernard; Fairweather, Graeme
1993
Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0768.65067
Fernandes, Ryan I.; Fairweather, Graeme
1993
Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0295.65062
Dendy, J. E. jun.; Fairweather, G.
1975
A high accuracy alternating direction method for the wave equation. Zbl 0221.65180
Fairweather, G.; Mitchell, A. R.
1965
Almost block diagonal linear systems: sequential and parallel solution techniques, and applications. Zbl 1051.65018
Amodio, P.; Cash, J. R.; Roussos, G.; Wright, R. W.; Fairweather, G.; Gladwell, I.; Kraut, G. L.; Paprzycki, M.
2000
A box method for a nonlinear equation of population dynamics. Zbl 0734.92023
Fairweather, G.; López-Marcos, J. C.
1991
On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method. Zbl 0397.65080
Fairweather, Graeme; Rizzo, Frank J.; Shippy, David J.; Wu, Yensen S.
1979
An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables. Zbl 0747.65082
Fernandes, Ryan I.; Fairweather, Graeme
1991
Some stable difference approximations to a fourth-order parabolic partial differential equation. Zbl 0147.13801
Fairweather, G.; Gourlay, A. R.
1967
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems. Zbl 1284.65026
Fernandes, Ryan I.; Fairweather, Graeme
2012
Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods. Zbl 1388.76359
Fairweather, Graeme; Lin, Qun; Lin, Yanping; Wang, Junping; Zhang, Shuhua
2006
Compact optimal quadratic spline collocation methods for the Helmholtz equation. Zbl 1218.65135
Fairweather, Graeme; Karageorghis, Andreas; Maack, Jon
2011
The method of fundamental solutions for transmission and scattering of elastic waves. Zbl 0825.73150
Kondapalli, Prasanna S.; Shippy, Davdi J.; Fairweather, Graeme
1992
The method of fundamental solutions for problems in potential theory. Zbl 0511.65087
Fairweather, Graeme; Johnston, R. L.
1982
Potential field based geometric modelling using the method of fundamental solutions. Zbl 1130.65035
Tankelevich, Roman; Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis
2006
Some high accuracy difference with a Splitting operator for equations of parabolic and elliptic type. Zbl 0148.39403
Fairweather, G.; Gourlay, A. R.; Mitchell, A. R.
1967
Orthogonal spline collocation methods for biharmonic problems. Zbl 0908.65103
Lou, Zhou-Ming; Bialecki, Bernard; Fairweather, Graeme
1998
Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems. Zbl 0820.65009
Bialecki, Bernard; Fairweather, Graeme
1995
Algorithm 704: ABDPACK and ABBPACK-FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65051
Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R.
1992
Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. Zbl 0722.76073
Shippy, D. J.; Kondapalli, P. S.; Fairweather, G.
1990
A note on the efficient implementation of certain Padé methods for linear parabolic problems. Zbl 0384.65036
Fairweather, Graeme
1978
A backward Euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation. Zbl 1352.65392
Fairweather, Graeme; Zhang, Haixiang; Yang, Xuehua; Xu, Da
2015
Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations. Zbl 1168.76037
Fairweather, Graeme; Ma, Heping; Sun, Weiwei
2008
Matrix decomposition algorithms for modified spline collocation for Helmholtz problems. Zbl 1035.65135
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas
2003
The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65050
Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R.
1992
On the eigenvalues and eigenvectors of a class of Hessenberg matrices. Zbl 0217.52603
Fairweather, G.
1971
Matrix decomposition algorithms for the $$C^{0}$$-quadratic finite element Galerkin method. Zbl 1176.65132
Du, Kui; Fairweather, Graeme; Nguyen, Que N.; Sun, Weiwei
2009
A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Zbl 1067.65135
Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis
2005
Galerkin and collocation methods for partial integro-differential equations. Zbl 0737.65103
Fairweather, G.
1991
A survey of higher-order methods for the numerical integration of semidiscrete parabolic problems. Zbl 0561.65087
Seward, W. L.; Fairweather, G.; Johnston, R. L.
1984
Galerkin method for vibration problems in two space variables. Zbl 0246.65031
Fairweather, Graeme
1972
Optimal superconvergent one step nodal cubic spline collocation methods. Zbl 1091.65118
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas
2005
An H$$^{1}$$-Galerkin mixed finite element method for an evolution equation with a positive-type memory term. Zbl 1047.65085
Pani, Amiya K.; Fairweather, Graeme
2002
An explicit extrapolated box scheme for the Gurtin-MacCamy equation. Zbl 0792.65108
Fairweather, G.; López-Marcos, J. C.
1994
A fourth-order cubic spline method for linear second-order two-point boundary-value problems. Zbl 0790.65078
Sloan, Ian H.; Tran, Dat; Fairweather, Graeme
1993
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains. Zbl 1352.65393
Fernandes, Ryan I.; Bialecki, Bernard; Fairweather, Graeme
2015
The Crank-Nicolson Hermite cubic orthogonal spline collocation method for the heat equation with nonlocal boundary conditions. Zbl 1279.80005
Bialecki, B.; Fairweather, G.; López-Marcos, J. C.
2013
Discrete-time orthogonal spline collocation methods for vibration problems. Zbl 1028.74022
Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
2002
Fourier methods for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0805.65107
Bialecki, Bernard; Fairweather, G.; Remington, K. A.
1994
On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112
Robinson, M. P.; Fairweather, G.; Herbst, B. M.
1993
The extrapolated Crank-Nicolson orthogonal spline collocation method for a quasilinear parabolic problem with nonlocal boundary conditions. Zbl 1309.65141
Bialecki, B.; Fairweather, G.; López-Marcos, J.
2015
Optimal superconvergent one step quadratic spline collocation methods. Zbl 1155.65089
Bialecki, B.; Fairweather, G.; Karageorghis, A.; Nguyen, Q. N.
2008
A new alternating direction method for parabolic equations in three space variables. Zbl 0137.33302
Fairweather, G.; Mitchell, A. R.
1965
An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105
Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G.
1994
Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems. Zbl 1360.76291
Robinson, Mark P.; Fairweather, Graeme
1993
Corrigenda. ’Some stable difference approximations to a fourth-order parabolic partial differential equation’, Math. Comp., v. 21, 1967, pp. 1-11. Zbl 0153.46405
Fairweather, G.; Gourlay, A. R.
1968
Matrix decomposition algorithms for arbitrary order $$C^0$$ tensor product finite element systems. Zbl 1297.65029
Du, Kui; Fairweather, Graeme; Sun, Weiwei
2015
Three-dimensional image reconstruction using the PF/MFS technique. Zbl 1244.65224
Tankelevich, R.; Fairweather, G.; Karageorghis, A.
2009
Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Zbl 1172.65062
Bialecki, Bernard; Fairweather, Graeme; Knudson, David B.; Lipman, D. Abram; Nguyen, Que N.; Sun, Weiwei; Weinberg, Gadalia M.
2009
Optimal superconvergent one step quadratic spline collocation methods for Helmholtz problems. Zbl 1157.65470
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Nguyen, Que N.
2008
Numerical integration. Recent developments, software and applications. (Proceedings of the NATO Advanced Research Workshop on Numerical Integration. Recent Developments, Software and Applications, Halifax, Canada, August 11-15, 1986). Zbl 0611.00023
Keast, Patrick (ed.); Fairweather, Graeme (ed.)
1987
A linear ADI method for the shallow-water equations. Zbl 0454.76032
Fairweather, G.; Navon, I. M.
1980
Alternating direction implicit Galerkin methods for an evolution equation with a positive-type memory term. Zbl 1328.65209
Khebchareon, Morrakot; Pani, Amiya K.; Fairweather, Graeme
2015
Direct numerical spline methods for first-order Fredholm integro- differential equations. Zbl 0799.65153
Micula, Gheorghe; Fairweather, Graeme
1993
Finite element methods for nonlinear parabolic and hyperbolic partial integro-differential equations. Zbl 0726.65160
Fairweather, Graeme; Yanik, Elizabeth G.
1989
A survey of spline collocation methods for the numerical solution of differential equations. Zbl 0679.65058
Fairweather, Graeme; Maede, Daniel
1989
On the approximate solution of a diffusion problem by Galerkin methods. Zbl 0428.65062
Fairweather, G.
1979
An investigation of Romberg quadrature. Zbl 0394.65008
Fairweather, Graeme; Keast, Pat
1978
On the extrapolation of Galerkin methods for parabolic problems. Zbl 0282.65080
Fairweather, G.; Johnson, J. P.
1975
Convergence analyses of Crank-Nicolson orthogonal spline collocation methods for linear parabolic problems in two space variables. Zbl 1347.65147
Khebchareon, Morrakot; Pani, Amiya Kumar; Fairweather, Graeme
2016
A Crank-Nicolson orthogonal spline collocation method for vibration problems. Zbl 0994.74081
Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
2000
Remark on algorithm 603. Zbl 0645.65017
Diaz, J. C.; Fairweather, G.; Keast, P.
1988
An assessment of numerical software for solving two-point boundary-value problems arising in heat transfer. Zbl 0619.76046
Fairweather, Graeme; Vedha-Nayagam, M.
1987
On the $$H^{-1}$$-Galerkin method for second-order linear two-point boundary value problems. Zbl 0546.65056
Fairweather, Graeme; Keast, Patrick; Diaz, Julio Cesar
1984
On the application of extrapolation, deferred correction and defect correction to discrete-time Galerkin methods for parabolic problems. Zbl 0573.65086
Fairweather, G.; Saylor, A. V.
1983
Errata: Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0331.65078
Dendy, J. E. jun.; Fairweather, G.
1976
A survey of discrete Galerkin methods for parabolic equations in one space variable. Zbl 0249.65068
Fairweather, Graeme
1972
Some computational results of an improved A. D. I. method for the Dirichlet problem. Zbl 0148.39404
Fairweather, G.; Mitchell, A. R.
1966
Convergence analyses of Crank-Nicolson orthogonal spline collocation methods for linear parabolic problems in two space variables. Zbl 1347.65147
Khebchareon, Morrakot; Pani, Amiya Kumar; Fairweather, Graeme
2016
An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation. Zbl 1328.65216
Fairweather, Graeme; Yang, Xuehua; Xu, Da; Zhang, Haixiang
2015
A backward Euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation. Zbl 1352.65392
Fairweather, Graeme; Zhang, Haixiang; Yang, Xuehua; Xu, Da
2015
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains. Zbl 1352.65393
Fernandes, Ryan I.; Bialecki, Bernard; Fairweather, Graeme
2015
The extrapolated Crank-Nicolson orthogonal spline collocation method for a quasilinear parabolic problem with nonlocal boundary conditions. Zbl 1309.65141
Bialecki, B.; Fairweather, G.; López-Marcos, J.
2015
Matrix decomposition algorithms for arbitrary order $$C^0$$ tensor product finite element systems. Zbl 1297.65029
Du, Kui; Fairweather, Graeme; Sun, Weiwei
2015
Alternating direction implicit Galerkin methods for an evolution equation with a positive-type memory term. Zbl 1328.65209
Khebchareon, Morrakot; Pani, Amiya K.; Fairweather, Graeme
2015
The Crank-Nicolson Hermite cubic orthogonal spline collocation method for the heat equation with nonlocal boundary conditions. Zbl 1279.80005
Bialecki, B.; Fairweather, G.; López-Marcos, J. C.
2013
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems. Zbl 1284.65026
Fernandes, Ryan I.; Fairweather, Graeme
2012
Matrix decomposition algorithms for elliptic boundary value problems: A survey. Zbl 1208.65036
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas
2011
Compact optimal quadratic spline collocation methods for the Helmholtz equation. Zbl 1218.65135
Fairweather, Graeme; Karageorghis, Andreas; Maack, Jon
2011
ADI orthogonal spline collocation methods for parabolic partial integro-differential equations. Zbl 1191.65186
Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I.
2010
Matrix decomposition algorithms for the $$C^{0}$$-quadratic finite element Galerkin method. Zbl 1176.65132
Du, Kui; Fairweather, Graeme; Nguyen, Que N.; Sun, Weiwei
2009
Three-dimensional image reconstruction using the PF/MFS technique. Zbl 1244.65224
Tankelevich, R.; Fairweather, G.; Karageorghis, A.
2009
Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Zbl 1172.65062
Bialecki, Bernard; Fairweather, Graeme; Knudson, David B.; Lipman, D. Abram; Nguyen, Que N.; Sun, Weiwei; Weinberg, Gadalia M.
2009
Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term. Zbl 1160.65068
Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I.
2008
Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations. Zbl 1168.76037
Fairweather, Graeme; Ma, Heping; Sun, Weiwei
2008
Optimal superconvergent one step quadratic spline collocation methods. Zbl 1155.65089
Bialecki, B.; Fairweather, G.; Karageorghis, A.; Nguyen, Q. N.
2008
Optimal superconvergent one step quadratic spline collocation methods for Helmholtz problems. Zbl 1157.65470
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Nguyen, Que N.
2008
Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods. Zbl 1388.76359
Fairweather, Graeme; Lin, Qun; Lin, Yanping; Wang, Junping; Zhang, Shuhua
2006
Potential field based geometric modelling using the method of fundamental solutions. Zbl 1130.65035
Tankelevich, Roman; Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis
2006
A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Zbl 1067.65135
Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis
2005
Optimal superconvergent one step nodal cubic spline collocation methods. Zbl 1091.65118
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas
2005
Algorithms for almost block diagonal linear systems. Zbl 1062.65031
2004
The method of fundamental solutions for scattering and radiation problems. Zbl 1060.76649
Fairweather, Graeme; Karageorghis, Andreas; Martin, P. A.
2003
Matrix decomposition algorithms for modified spline collocation for Helmholtz problems. Zbl 1035.65135
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas
2003
$$H^1$$-Galerkin mixed finite element methods for parabolic partial integro-differential equations. Zbl 1008.65101
Pani, Amiya K.; Fairweather, Graeme
2002
An H$$^{1}$$-Galerkin mixed finite element method for an evolution equation with a positive-type memory term. Zbl 1047.65085
Pani, Amiya K.; Fairweather, Graeme
2002
Discrete-time orthogonal spline collocation methods for vibration problems. Zbl 1028.74022
Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
2002
Orthogonal spline collocation methods for partial differential equations. Zbl 0971.65105
Bialecki, B.; Fairweather, G.
2001
The method of fundamental solutions for axisymmetric elasticity problems. Zbl 1011.74005
Karageorghis, A.; Fairweather, G.
2000
Almost block diagonal linear systems: sequential and parallel solution techniques, and applications. Zbl 1051.65018
Amodio, P.; Cash, J. R.; Roussos, G.; Wright, R. W.; Fairweather, G.; Gladwell, I.; Kraut, G. L.; Paprzycki, M.
2000
A Crank-Nicolson orthogonal spline collocation method for vibration problems. Zbl 0994.74081
Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
2000
The method of fundamental solutions for axisymmetric potential problems. Zbl 0932.74078
Karageorghis, Andreas; Fairweather, Graeme
1999
The method of fundamental solutions for elliptic boundary value problems. Zbl 0922.65074
Fairweather, Graeme; Karageorghis, Andreas
1998
Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. Zbl 0911.65095
Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard
1998
Orthogonal spline collocation methods for biharmonic problems. Zbl 0908.65103
Lou, Zhou-Ming; Bialecki, Bernard; Fairweather, Graeme
1998
Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Zbl 0868.65068
Fairweather, G.; López-Marcos, J. C.
1996
Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems. Zbl 0820.65009
Bialecki, Bernard; Fairweather, Graeme
1995
Orthogonal spline collocation methods for Schrödinger-type equations in one space variable. Zbl 0806.65123
Robinson, Mark P.; Fairweather, Graeme
1994
Spline collocation methods for a class of hyperbolic partial integro- differential equations. Zbl 0814.65137
Fairweather, Graeme
1994
An explicit extrapolated box scheme for the Gurtin-MacCamy equation. Zbl 0792.65108
Fairweather, G.; López-Marcos, J. C.
1994
Fourier methods for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0805.65107
Bialecki, Bernard; Fairweather, G.; Remington, K. A.
1994
An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105
Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G.
1994
Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. Zbl 0781.65031
Bialecki, Bernard; Fairweather, Graeme
1993
Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0768.65067
Fernandes, Ryan I.; Fairweather, Graeme
1993
A fourth-order cubic spline method for linear second-order two-point boundary-value problems. Zbl 0790.65078
Sloan, Ian H.; Tran, Dat; Fairweather, Graeme
1993
On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112
Robinson, M. P.; Fairweather, G.; Herbst, B. M.
1993
Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems. Zbl 1360.76291
Robinson, Mark P.; Fairweather, Graeme
1993
Direct numerical spline methods for first-order Fredholm integro- differential equations. Zbl 0799.65153
Micula, Gheorghe; Fairweather, Graeme
1993
Orthogonal spline collocation methods for some partial integrodifferential equations. Zbl 0756.65157
Yan, Yi; Fairweather, Graeme
1992
Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations. Zbl 0752.65076
Bialecki, Bernard; Fairweather, Graeme; Bennett, Karin R.
1992
The method of fundamental solutions for transmission and scattering of elastic waves. Zbl 0825.73150
Kondapalli, Prasanna S.; Shippy, Davdi J.; Fairweather, Graeme
1992
Algorithm 704: ABDPACK and ABBPACK-FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65051
Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R.
1992
The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65050
Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R.
1992
The reformulation and numerical solution of certain nonclassical initial- boundary value problems. Zbl 0722.65062
Fairweather, Graeme; Saylor, Rick D.
1991
A box method for a nonlinear equation of population dynamics. Zbl 0734.92023
Fairweather, G.; López-Marcos, J. C.
1991
An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables. Zbl 0747.65082
Fernandes, Ryan I.; Fairweather, Graeme
1991
Galerkin and collocation methods for partial integro-differential equations. Zbl 0737.65103
Fairweather, G.
1991
Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. Zbl 0722.76073
Shippy, D. J.; Kondapalli, P. S.; Fairweather, G.
1990
The simple layer potential method of fundamental solutions for certain biharmonic problems. Zbl 0687.76028
Karageorghis, Andreas; Fairweather, Graeme
1989
The method of fundamental solutions for the solution of nonlinear plane potential problems. Zbl 0676.65110
Karageorghis, A.; Fairweather, G.
1989
Finite element methods for nonlinear parabolic and hyperbolic partial integro-differential equations. Zbl 0726.65160
Fairweather, Graeme; Yanik, Elizabeth G.
1989
A survey of spline collocation methods for the numerical solution of differential equations. Zbl 0679.65058
Fairweather, Graeme; Maede, Daniel
1989
Finite element methods for parabolic and hyperbolic partial integro- differential equations. Zbl 0657.65142
Yanik, Elizabeth G.; Fairweather, Graeme
1988
The Almansi method of fundamental solutions for solving biharmonic problems. Zbl 0639.65066
Karageorghis, Andreas; Fairweather, Graeme
1988
Remark on algorithm 603. Zbl 0645.65017
Diaz, J. C.; Fairweather, G.; Keast, P.
1988
The method of fundamental solutions for the numerical solution of the biharmonic equation. Zbl 0618.65108
Karageorghis, Andreas; Fairweather, Graeme
1987
Numerical integration. Recent developments, software and applications. (Proceedings of the NATO Advanced Research Workshop on Numerical Integration. Recent Developments, Software and Applications, Halifax, Canada, August 11-15, 1986). Zbl 0611.00023
Keast, Patrick (ed.); Fairweather, Graeme (ed.)
1987
An assessment of numerical software for solving two-point boundary-value problems arising in heat transfer. Zbl 0619.76046
Fairweather, Graeme; Vedha-Nayagam, M.
1987
Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0595.65122
Greenwell-Yanik, C. E.; Fairweather, G.
1986
The method of fundamental solutions for problems in potential flow. Zbl 0546.76021
Johnston, R. L.; Fairweather, G.
1984
A survey of higher-order methods for the numerical integration of semidiscrete parabolic problems. Zbl 0561.65087
Seward, W. L.; Fairweather, G.; Johnston, R. L.
1984
On the $$H^{-1}$$-Galerkin method for second-order linear two-point boundary value problems. Zbl 0546.65056
Fairweather, Graeme; Keast, Patrick; Diaz, Julio Cesar
1984
FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. Zbl 0516.65013
Diaz, J. C.; Fairweather, G.; Keast, P.
1983
On the application of extrapolation, deferred correction and defect correction to discrete-time Galerkin methods for parabolic problems. Zbl 0573.65086
Fairweather, G.; Saylor, A. V.
1983
The method of fundamental solutions for problems in potential theory. Zbl 0511.65087
Fairweather, Graeme; Johnston, R. L.
1982
A linear ADI method for the shallow-water equations. Zbl 0454.76032
Fairweather, G.; Navon, I. M.
1980
On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method. Zbl 0397.65080
Fairweather, Graeme; Rizzo, Frank J.; Shippy, David J.; Wu, Yensen S.
1979
On the approximate solution of a diffusion problem by Galerkin methods. Zbl 0428.65062
Fairweather, G.
1979
Finite element Galerkin methods for differential equations. Zbl 0372.65044
Fairweather, Graeme
1978
A note on the efficient implementation of certain Padé methods for linear parabolic problems. Zbl 0384.65036
Fairweather, Graeme
1978
An investigation of Romberg quadrature. Zbl 0394.65008
Fairweather, Graeme; Keast, Pat
1978
Errata: Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0331.65078
Dendy, J. E. jun.; Fairweather, G.
1976
Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0295.65062
Dendy, J. E. jun.; Fairweather, G.
1975
On the extrapolation of Galerkin methods for parabolic problems. Zbl 0282.65080
Fairweather, G.; Johnson, J. P.
1975
Three-level Galerkin methods for parabolic equations. Zbl 0313.65107
Dupont, Todd; Fairweather, Graeme; Johnson, J. Peter
1974
Galerkin method for vibration problems in two space variables. Zbl 0246.65031
Fairweather, Graeme
1972
A survey of discrete Galerkin methods for parabolic equations in one space variable. Zbl 0249.65068
Fairweather, Graeme
1972
On the eigenvalues and eigenvectors of a class of Hessenberg matrices. Zbl 0217.52603
Fairweather, G.
1971
Corrigenda. ’Some stable difference approximations to a fourth-order parabolic partial differential equation’, Math. Comp., v. 21, 1967, pp. 1-11. Zbl 0153.46405
Fairweather, G.; Gourlay, A. R.
1968
A new computational procedure for A.D.I. methods. Zbl 0252.65072
Fairweather, G.; Mitchell, A. R.
1967
Some stable difference approximations to a fourth-order parabolic partial differential equation. Zbl 0147.13801
Fairweather, G.; Gourlay, A. R.
1967
Some high accuracy difference with a Splitting operator for equations of parabolic and elliptic type. Zbl 0148.39403
Fairweather, G.; Gourlay, A. R.; Mitchell, A. R.
1967
Some computational results of an improved A. D. I. method for the Dirichlet problem. Zbl 0148.39404
Fairweather, G.; Mitchell, A. R.
1966
A high accuracy alternating direction method for the wave equation. Zbl 0221.65180
Fairweather, G.; Mitchell, A. R.
1965
A new alternating direction method for parabolic equations in three space variables. Zbl 0137.33302
Fairweather, G.; Mitchell, A. R.
1965
Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations. Zbl 0123.12001
Mitchell, A. R.; Fairweather, G.
1964
all top 5

#### Cited by 1,540 Authors

 61 Karageorghis, Andreas 39 Xu, Da 38 Chen, Ching-Shyang 34 Fairweather, Graeme 33 Chen, Wen 27 Bialecki, Bernard 27 Lesnic, Daniel 25 Marin, Liviu 22 Dehghan Takht Fooladi, Mehdi 19 Li, Zi-Cai 17 Smyrlis, Yiorgos-Sokratis 16 Gu, Yan 15 Fu, Zhuojia 14 Alves, Carlos J. S. 14 Johansson, B. Tomas 14 Yang, Xuehua 13 Li, Jichun 13 Lin, Ji 13 Pani, Amiya Kumar 13 Zhang, Haixiang 12 Qin, Qinghua 12 Young, Dennis L. 11 Jorge, Juan Carlos 11 Šarler, Božidar 11 Sun, Weiwei 11 Tsai, Chia-Cheng 10 Cheng, Alexander H.-D. 9 Fan, Chia-Ming 9 Godinho, Luís M. C. 9 Kolodziej, Jan Adam 9 Potier-Ferry, Michel 9 Qu, Wenzhen 9 Shi, Dongyang 9 Young, Der-Liang 8 Bujanda, Blanca 8 He, Yinnian 8 Huang, Hung-Tsai 8 Khaliq, Abdul Q. M. 8 Sinha, Rajen Kumar 8 Tadeu, António J. B. 8 Wang, Fajie 8 Zhang, Chuanzeng 7 Doha, Eid H. 7 Du, Kui 7 Lin, Yanping 7 Liu, Xiaoyan 7 Mitchell, Andrew Ronald 7 Mustapha, Kassem 7 Ramachandran, Palghat A. 7 Reeve, Thomas 7 Sun, Linlin 7 Wang, Hui 7 Wei, Ting 6 Abbasbandy, Saeid 6 Abou-Dina, Moustafa S. 6 Boroomand, Bijan 6 Chen, Wen 6 Danumjaya, Palla 6 Grabski, Jakub Krzysztof 6 Hon, Yiu-Chung 6 Li, Xiaolin 6 Liu, Chein-Shan 6 Liu, Qingguo 6 Mohanty, Ranjan Kumar 6 Muir, Paul H. 6 Reutskiy, Sergiy Yu 6 Sapagovas, Mifodijus 6 Sun, Yao 6 Valtchev, Svilen S. 6 Wei, Xing 6 Whiteman, John Robert 5 Balakrishnan, Karthik 5 Berger, J. R. 5 Chen, Jeng-Tzong 5 Chiang, John Y. 5 Fernandes, Ryan I. 5 Gourlay, A. R. 5 Lee, Ming-Gong 5 Ling, Leevan 5 López-Marcos, Juan Carlos 5 Martins, Nuno F. M. 5 McLean, William 5 Rashed, Youssef F. 5 Thomée, Vidar 5 Yamamoto, Masahiro 5 Yang, Fenglian 5 Yuan, Yirang 5 Zhou, Zhaojie 4 António, Julieta M. P. 4 Antunes, Pedro Ricardo Simão 4 Aziz, Imran 4 Brunner, Hermann 4 Croisille, Jean-Pierre 4 Dou, Fangfang 4 Fan, Chen-Ming 4 Fan, Cheng-Ming 4 Fan, Congmin 4 Ganesh, Madhu 4 Golberg, Michael A. 4 Hadjidimos, Apostolos ...and 1,440 more Authors
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#### Cited in 159 Serials

 231 Engineering Analysis with Boundary Elements 86 Journal of Computational and Applied Mathematics 83 Computers & Mathematics with Applications 68 Applied Mathematics and Computation 57 Journal of Computational Physics 46 Applied Numerical Mathematics 38 Computer Methods in Applied Mechanics and Engineering 38 Numerical Methods for Partial Differential Equations 30 Applied Mathematical Modelling 29 Journal of Scientific Computing 29 International Journal of Computer Mathematics 27 Numerical Algorithms 21 Inverse Problems in Science and Engineering 20 Numerische Mathematik 18 Mathematics of Computation 18 Advances in Computational Mathematics 15 Computational Mechanics 14 International Journal for Numerical Methods in Engineering 11 Applied Mathematics Letters 10 Mathematical Problems in Engineering 9 Computing 9 Mathematics and Computers in Simulation 9 Mathematical and Computer Modelling 8 BIT 8 Journal of Integral Equations and Applications 7 Applicable Analysis 7 Journal of Mathematical Analysis and Applications 7 Journal of Applied Mathematics and Computing 7 International Journal of Computational Methods 6 International Journal for Numerical Methods in Fluids 6 SIAM Journal on Numerical Analysis 6 Communications in Numerical Methods in Engineering 6 Advances in Difference Equations 5 Numerical Functional Analysis and Optimization 5 Acta Mathematicae Applicatae Sinica. English Series 5 Computational and Applied Mathematics 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 BIT. Nordisk Tidskrift for Informationsbehandling 4 Computers and Fluids 4 Journal of Engineering Mathematics 4 Lithuanian Mathematical Journal 4 Calcolo 4 Applied Mathematics and Mechanics. (English Edition) 4 Linear Algebra and its Applications 4 SIAM Journal on Scientific Computing 4 Abstract and Applied Analysis 4 Nonlinear Analysis. Real World Applications 3 Archive for Rational Mechanics and Analysis 3 International Journal of Heat and Mass Transfer 3 International Journal of Solids and Structures 3 Journal of Fluid Mechanics 3 Journal of Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Chaos, Solitons and Fractals 3 International Journal of Mathematics and Mathematical Sciences 3 Japan Journal of Industrial and Applied Mathematics 3 Applications of Mathematics 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Discrete Dynamics in Nature and Society 3 Advances in Numerical Analysis 2 Journal of Mathematical Biology 2 Wave Motion 2 Journal of Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 RAIRO. Analyse Numérique 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Computational Mathematics and Mathematical Physics 2 Advances in Engineering Software 2 Physics of Fluids 2 Numerical Linear Algebra with Applications 2 International Journal of Numerical Methods for Heat & Fluid Flow 2 Journal of the Egyptian Mathematical Society 2 Journal of Difference Equations and Applications 2 Mathematics and Mechanics of Solids 2 European Journal of Mechanics. B. Fluids 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 The ANZIAM Journal 2 Differential Equations 2 Archives of Computational Methods in Engineering 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 Discrete and Continuous Dynamical Systems. Series S 2 International Journal of Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications 1 Computer Physics Communications 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Franklin Institute 1 Mathematical Biosciences 1 Mathematische Semesterberichte 1 Physics Letters. A 1 Physics of Fluids, A 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Aplikace Matematiky 1 Applied Mathematics and Optimization 1 Collectanea Mathematica 1 Journal of Approximation Theory 1 Kybernetika 1 Meccanica 1 Mechanics Research Communications 1 Proceedings of the American Mathematical Society ...and 59 more Serials
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#### Cited in 38 Fields

 1,028 Numerical analysis (65-XX) 550 Partial differential equations (35-XX) 190 Mechanics of deformable solids (74-XX) 156 Fluid mechanics (76-XX) 114 Integral equations (45-XX) 58 Classical thermodynamics, heat transfer (80-XX) 44 Ordinary differential equations (34-XX) 36 Optics, electromagnetic theory (78-XX) 25 Biology and other natural sciences (92-XX) 19 Approximations and expansions (41-XX) 17 Real functions (26-XX) 14 Potential theory (31-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Geophysics (86-XX) 9 Systems theory; control (93-XX) 8 Functions of a complex variable (30-XX) 7 Quantum theory (81-XX) 6 Operations research, mathematical programming (90-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Integral transforms, operational calculus (44-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Combinatorics (05-XX) 4 Functional analysis (46-XX) 4 Operator theory (47-XX) 4 Probability theory and stochastic processes (60-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 3 Number theory (11-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Difference and functional equations (39-XX) 1 Information and communication theory, circuits (94-XX)