Edit Profile Fairweather, Graeme Compute Distance To: Compute Author ID: fairweather.graeme Published as: Fairweather, G.; Fairweather, Graeme Documents Indexed: 120 Publications since 1964, including 5 Books all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0922.65074Fairweather, Graeme; Karageorghis, Andreas 420 1998 The method of fundamental solutions for scattering and radiation problems. Zbl 1060.76649Fairweather, Graeme; Karageorghis, Andreas; Martin, P. A. 112 2003 The method of fundamental solutions for the numerical solution of the biharmonic equation. Zbl 0618.65108Karageorghis, Andreas; Fairweather, Graeme 98 1987 Finite element methods for parabolic and hyperbolic partial integro- differential equations. Zbl 0657.65142Yanik, Elizabeth G.; Fairweather, Graeme 69 1988 Finite element Galerkin methods for differential equations. Zbl 0372.65044Fairweather, Graeme 66 1978 Orthogonal spline collocation methods for partial differential equations. Zbl 0971.65105Bialecki, B.; Fairweather, G. 45 2001 \(H^1\)-Galerkin mixed finite element methods for parabolic partial integro-differential equations. Zbl 1008.65101Pani, Amiya K.; Fairweather, Graeme 41 2002 A new computational procedure for A.D.I. methods. Zbl 0252.65072Fairweather, G.; Mitchell, A. R. 40 1967 FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. Zbl 0516.65013Diaz, J. C.; Fairweather, G.; Keast, P. 38 1983 The method of fundamental solutions for problems in potential flow. Zbl 0546.76021Johnston, R. L.; Fairweather, G. 34 1984 Orthogonal spline collocation methods for Schrödinger-type equations in one space variable. Zbl 0806.65123Robinson, Mark P.; Fairweather, Graeme 33 1994 The reformulation and numerical solution of certain nonclassical initial- boundary value problems. Zbl 0722.65062Fairweather, Graeme; Saylor, Rick D. 33 1991 Three-level Galerkin methods for parabolic equations. Zbl 0313.65107Dupont, Todd; Fairweather, Graeme; Johnson, J. Peter 33 1974 The method of fundamental solutions for axisymmetric elasticity problems. Zbl 1011.74005Karageorghis, A.; Fairweather, G. 32 2000 Orthogonal spline collocation methods for some partial integrodifferential equations. Zbl 0756.65157Yan, Yi; Fairweather, Graeme 32 1992 The method of fundamental solutions for axisymmetric potential problems. Zbl 0932.74078Karageorghis, Andreas; Fairweather, Graeme 30 1999 Matrix decomposition algorithms for elliptic boundary value problems: A survey. Zbl 1208.65036Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 26 2011 Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Zbl 0868.65068Fairweather, G.; López-Marcos, J. C. 25 1996 Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0595.65122Greenwell-Yanik, C. E.; Fairweather, G. 25 1986 Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations. Zbl 0123.12001Mitchell, A. R.; Fairweather, G. 23 1964 Spline collocation methods for a class of hyperbolic partial integro- differential equations. Zbl 0814.65137Fairweather, Graeme 22 1994 ADI orthogonal spline collocation methods for parabolic partial integro-differential equations. Zbl 1191.65186Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 21 2010 Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term. Zbl 1160.65068Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 21 2008 Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations. Zbl 0752.65076Bialecki, Bernard; Fairweather, Graeme; Bennett, Karin R. 21 1992 The simple layer potential method of fundamental solutions for certain biharmonic problems. Zbl 0687.76028Karageorghis, Andreas; Fairweather, Graeme 21 1989 The method of fundamental solutions for the solution of nonlinear plane potential problems. Zbl 0676.65110Karageorghis, A.; Fairweather, G. 21 1989 The Almansi method of fundamental solutions for solving biharmonic problems. Zbl 0639.65066Karageorghis, Andreas; Fairweather, Graeme 21 1988 Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. Zbl 0911.65095Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 19 1998 An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation. Zbl 1328.65216Fairweather, Graeme; Yang, Xuehua; Xu, Da; Zhang, Haixiang 18 2015 Algorithms for almost block diagonal linear systems. Zbl 1062.65031Fairweather, Graeme; Gladwell, Ian 18 2004 Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. Zbl 0781.65031Bialecki, Bernard; Fairweather, Graeme 18 1993 Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0768.65067Fernandes, Ryan I.; Fairweather, Graeme 18 1993 Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0295.65062Dendy, J. E. jun.; Fairweather, G. 18 1975 A high accuracy alternating direction method for the wave equation. Zbl 0221.65180Fairweather, G.; Mitchell, A. R. 18 1965 Almost block diagonal linear systems: sequential and parallel solution techniques, and applications. Zbl 1051.65018Amodio, P.; Cash, J. R.; Roussos, G.; Wright, R. W.; Fairweather, G.; Gladwell, I.; Kraut, G. L.; Paprzycki, M. 15 2000 A box method for a nonlinear equation of population dynamics. Zbl 0734.92023Fairweather, G.; López-Marcos, J. C. 15 1991 On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method. Zbl 0397.65080Fairweather, Graeme; Rizzo, Frank J.; Shippy, David J.; Wu, Yensen S. 15 1979 An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables. Zbl 0747.65082Fernandes, Ryan I.; Fairweather, Graeme 14 1991 Some stable difference approximations to a fourth-order parabolic partial differential equation. Zbl 0147.13801Fairweather, G.; Gourlay, A. R. 14 1967 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems. Zbl 1284.65026Fernandes, Ryan I.; Fairweather, Graeme 13 2012 Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods. Zbl 1388.76359Fairweather, Graeme; Lin, Qun; Lin, Yanping; Wang, Junping; Zhang, Shuhua 13 2006 Compact optimal quadratic spline collocation methods for the Helmholtz equation. Zbl 1218.65135Fairweather, Graeme; Karageorghis, Andreas; Maack, Jon 12 2011 The method of fundamental solutions for transmission and scattering of elastic waves. Zbl 0825.73150Kondapalli, Prasanna S.; Shippy, Davdi J.; Fairweather, Graeme 12 1992 The method of fundamental solutions for problems in potential theory. Zbl 0511.65087Fairweather, Graeme; Johnston, R. L. 12 1982 Potential field based geometric modelling using the method of fundamental solutions. Zbl 1130.65035Tankelevich, Roman; Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 11 2006 Some high accuracy difference with a Splitting operator for equations of parabolic and elliptic type. Zbl 0148.39403Fairweather, G.; Gourlay, A. R.; Mitchell, A. R. 11 1967 Orthogonal spline collocation methods for biharmonic problems. Zbl 0908.65103Lou, Zhou-Ming; Bialecki, Bernard; Fairweather, Graeme 10 1998 Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems. Zbl 0820.65009Bialecki, Bernard; Fairweather, Graeme 10 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 0892.65051Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 10 1992 Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. Zbl 0722.76073Shippy, D. J.; Kondapalli, P. S.; Fairweather, G. 10 1990 A note on the efficient implementation of certain Padé methods for linear parabolic problems. Zbl 0384.65036Fairweather, Graeme 10 1978 A backward Euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation. Zbl 1352.65392Fairweather, Graeme; Zhang, Haixiang; Yang, Xuehua; Xu, Da 9 2015 Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations. Zbl 1168.76037Fairweather, Graeme; Ma, Heping; Sun, Weiwei 9 2008 Matrix decomposition algorithms for modified spline collocation for Helmholtz problems. Zbl 1035.65135Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 9 2003 The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65050Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 9 1992 On the eigenvalues and eigenvectors of a class of Hessenberg matrices. Zbl 0217.52603Fairweather, G. 9 1971 Matrix decomposition algorithms for the \(C^{0}\)-quadratic finite element Galerkin method. Zbl 1176.65132Du, Kui; Fairweather, Graeme; Nguyen, Que N.; Sun, Weiwei 8 2009 A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Zbl 1067.65135Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 8 2005 Galerkin and collocation methods for partial integro-differential equations. Zbl 0737.65103Fairweather, G. 8 1991 A survey of higher-order methods for the numerical integration of semidiscrete parabolic problems. Zbl 0561.65087Seward, W. L.; Fairweather, G.; Johnston, R. L. 8 1984 Galerkin method for vibration problems in two space variables. Zbl 0246.65031Fairweather, Graeme 8 1972 Optimal superconvergent one step nodal cubic spline collocation methods. Zbl 1091.65118Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 7 2005 An H\(^{1}\)-Galerkin mixed finite element method for an evolution equation with a positive-type memory term. Zbl 1047.65085Pani, Amiya K.; Fairweather, Graeme 7 2002 An explicit extrapolated box scheme for the Gurtin-MacCamy equation. Zbl 0792.65108Fairweather, G.; López-Marcos, J. C. 7 1994 A fourth-order cubic spline method for linear second-order two-point boundary-value problems. Zbl 0790.65078Sloan, Ian H.; Tran, Dat; Fairweather, Graeme 7 1993 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains. Zbl 1352.65393Fernandes, Ryan I.; Bialecki, Bernard; Fairweather, Graeme 6 2015 The Crank-Nicolson Hermite cubic orthogonal spline collocation method for the heat equation with nonlocal boundary conditions. Zbl 1279.80005Bialecki, B.; Fairweather, G.; López-Marcos, J. C. 6 2013 Discrete-time orthogonal spline collocation methods for vibration problems. Zbl 1028.74022Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 6 2002 Fourier methods for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0805.65107Bialecki, Bernard; Fairweather, G.; Remington, K. A. 6 1994 On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112Robinson, M. P.; Fairweather, G.; Herbst, B. M. 6 1993 The extrapolated Crank-Nicolson orthogonal spline collocation method for a quasilinear parabolic problem with nonlocal boundary conditions. Zbl 1309.65141Bialecki, B.; Fairweather, G.; López-Marcos, J. 5 2015 Optimal superconvergent one step quadratic spline collocation methods. Zbl 1155.65089Bialecki, B.; Fairweather, G.; Karageorghis, A.; Nguyen, Q. N. 5 2008 A new alternating direction method for parabolic equations in three space variables. Zbl 0137.33302Fairweather, G.; Mitchell, A. R. 5 1965 An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G. 4 1994 Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems. Zbl 1360.76291Robinson, Mark P.; Fairweather, Graeme 4 1993 Corrigenda. ’Some stable difference approximations to a fourth-order parabolic partial differential equation’, Math. Comp., v. 21, 1967, pp. 1-11. Zbl 0153.46405Fairweather, G.; Gourlay, A. R. 4 1968 Matrix decomposition algorithms for arbitrary order \(C^0\) tensor product finite element systems. Zbl 1297.65029Du, Kui; Fairweather, Graeme; Sun, Weiwei 3 2015 Three-dimensional image reconstruction using the PF/MFS technique. Zbl 1244.65224Tankelevich, R.; Fairweather, G.; Karageorghis, A. 3 2009 Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Zbl 1172.65062Bialecki, Bernard; Fairweather, Graeme; Knudson, David B.; Lipman, D. Abram; Nguyen, Que N.; Sun, Weiwei; Weinberg, Gadalia M. 3 2009 Optimal superconvergent one step quadratic spline collocation methods for Helmholtz problems. Zbl 1157.65470Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Nguyen, Que N. 3 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 0611.00023Keast, Patrick (ed.); Fairweather, Graeme (ed.) 3 1987 A linear ADI method for the shallow-water equations. Zbl 0454.76032Fairweather, G.; Navon, I. M. 3 1980 Alternating direction implicit Galerkin methods for an evolution equation with a positive-type memory term. Zbl 1328.65209Khebchareon, Morrakot; Pani, Amiya K.; Fairweather, Graeme 2 2015 Direct numerical spline methods for first-order Fredholm integro- differential equations. Zbl 0799.65153Micula, Gheorghe; Fairweather, Graeme 2 1993 Finite element methods for nonlinear parabolic and hyperbolic partial integro-differential equations. Zbl 0726.65160Fairweather, Graeme; Yanik, Elizabeth G. 2 1989 A survey of spline collocation methods for the numerical solution of differential equations. Zbl 0679.65058Fairweather, Graeme; Maede, Daniel 2 1989 On the approximate solution of a diffusion problem by Galerkin methods. Zbl 0428.65062Fairweather, G. 2 1979 An investigation of Romberg quadrature. Zbl 0394.65008Fairweather, Graeme; Keast, Pat 2 1978 On the extrapolation of Galerkin methods for parabolic problems. Zbl 0282.65080Fairweather, G.; Johnson, J. P. 2 1975 Convergence analyses of Crank-Nicolson orthogonal spline collocation methods for linear parabolic problems in two space variables. Zbl 1347.65147Khebchareon, Morrakot; Pani, Amiya Kumar; Fairweather, Graeme 1 2016 A Crank-Nicolson orthogonal spline collocation method for vibration problems. Zbl 0994.74081Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 1 2000 Remark on algorithm 603. Zbl 0645.65017Diaz, J. C.; Fairweather, G.; Keast, P. 1 1988 An assessment of numerical software for solving two-point boundary-value problems arising in heat transfer. Zbl 0619.76046Fairweather, Graeme; Vedha-Nayagam, M. 1 1987 On the \(H^{-1}\)-Galerkin method for second-order linear two-point boundary value problems. Zbl 0546.65056Fairweather, Graeme; Keast, Patrick; Diaz, Julio Cesar 1 1984 On the application of extrapolation, deferred correction and defect correction to discrete-time Galerkin methods for parabolic problems. Zbl 0573.65086Fairweather, G.; Saylor, A. V. 1 1983 Errata: Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0331.65078Dendy, J. E. jun.; Fairweather, G. 1 1976 A survey of discrete Galerkin methods for parabolic equations in one space variable. Zbl 0249.65068Fairweather, Graeme 1 1972 Some computational results of an improved A. D. I. method for the Dirichlet problem. Zbl 0148.39404Fairweather, G.; Mitchell, A. R. 1 1966 Convergence analyses of Crank-Nicolson orthogonal spline collocation methods for linear parabolic problems in two space variables. Zbl 1347.65147Khebchareon, Morrakot; Pani, Amiya Kumar; Fairweather, Graeme 1 2016 An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation. Zbl 1328.65216Fairweather, Graeme; Yang, Xuehua; Xu, Da; Zhang, Haixiang 18 2015 A backward Euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation. Zbl 1352.65392Fairweather, Graeme; Zhang, Haixiang; Yang, Xuehua; Xu, Da 9 2015 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains. Zbl 1352.65393Fernandes, Ryan I.; Bialecki, Bernard; Fairweather, Graeme 6 2015 The extrapolated Crank-Nicolson orthogonal spline collocation method for a quasilinear parabolic problem with nonlocal boundary conditions. Zbl 1309.65141Bialecki, B.; Fairweather, G.; López-Marcos, J. 5 2015 Matrix decomposition algorithms for arbitrary order \(C^0\) tensor product finite element systems. Zbl 1297.65029Du, Kui; Fairweather, Graeme; Sun, Weiwei 3 2015 Alternating direction implicit Galerkin methods for an evolution equation with a positive-type memory term. Zbl 1328.65209Khebchareon, Morrakot; Pani, Amiya K.; Fairweather, Graeme 2 2015 The Crank-Nicolson Hermite cubic orthogonal spline collocation method for the heat equation with nonlocal boundary conditions. Zbl 1279.80005Bialecki, B.; Fairweather, G.; López-Marcos, J. C. 6 2013 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems. Zbl 1284.65026Fernandes, Ryan I.; Fairweather, Graeme 13 2012 Matrix decomposition algorithms for elliptic boundary value problems: A survey. Zbl 1208.65036Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 26 2011 Compact optimal quadratic spline collocation methods for the Helmholtz equation. Zbl 1218.65135Fairweather, Graeme; Karageorghis, Andreas; Maack, Jon 12 2011 ADI orthogonal spline collocation methods for parabolic partial integro-differential equations. Zbl 1191.65186Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 21 2010 Matrix decomposition algorithms for the \(C^{0}\)-quadratic finite element Galerkin method. Zbl 1176.65132Du, Kui; Fairweather, Graeme; Nguyen, Que N.; Sun, Weiwei 8 2009 Three-dimensional image reconstruction using the PF/MFS technique. Zbl 1244.65224Tankelevich, R.; Fairweather, G.; Karageorghis, A. 3 2009 Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Zbl 1172.65062Bialecki, Bernard; Fairweather, Graeme; Knudson, David B.; Lipman, D. Abram; Nguyen, Que N.; Sun, Weiwei; Weinberg, Gadalia M. 3 2009 Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term. Zbl 1160.65068Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 21 2008 Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations. Zbl 1168.76037Fairweather, Graeme; Ma, Heping; Sun, Weiwei 9 2008 Optimal superconvergent one step quadratic spline collocation methods. Zbl 1155.65089Bialecki, B.; Fairweather, G.; Karageorghis, A.; Nguyen, Q. N. 5 2008 Optimal superconvergent one step quadratic spline collocation methods for Helmholtz problems. Zbl 1157.65470Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Nguyen, Que N. 3 2008 Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods. Zbl 1388.76359Fairweather, Graeme; Lin, Qun; Lin, Yanping; Wang, Junping; Zhang, Shuhua 13 2006 Potential field based geometric modelling using the method of fundamental solutions. Zbl 1130.65035Tankelevich, Roman; Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 11 2006 A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Zbl 1067.65135Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 8 2005 Optimal superconvergent one step nodal cubic spline collocation methods. Zbl 1091.65118Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 7 2005 Algorithms for almost block diagonal linear systems. Zbl 1062.65031Fairweather, Graeme; Gladwell, Ian 18 2004 The method of fundamental solutions for scattering and radiation problems. Zbl 1060.76649Fairweather, Graeme; Karageorghis, Andreas; Martin, P. A. 112 2003 Matrix decomposition algorithms for modified spline collocation for Helmholtz problems. Zbl 1035.65135Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 9 2003 \(H^1\)-Galerkin mixed finite element methods for parabolic partial integro-differential equations. Zbl 1008.65101Pani, Amiya K.; Fairweather, Graeme 41 2002 An H\(^{1}\)-Galerkin mixed finite element method for an evolution equation with a positive-type memory term. Zbl 1047.65085Pani, Amiya K.; Fairweather, Graeme 7 2002 Discrete-time orthogonal spline collocation methods for vibration problems. Zbl 1028.74022Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 6 2002 Orthogonal spline collocation methods for partial differential equations. Zbl 0971.65105Bialecki, B.; Fairweather, G. 45 2001 The method of fundamental solutions for axisymmetric elasticity problems. Zbl 1011.74005Karageorghis, A.; Fairweather, G. 32 2000 Almost block diagonal linear systems: sequential and parallel solution techniques, and applications. Zbl 1051.65018Amodio, P.; Cash, J. R.; Roussos, G.; Wright, R. W.; Fairweather, G.; Gladwell, I.; Kraut, G. L.; Paprzycki, M. 15 2000 A Crank-Nicolson orthogonal spline collocation method for vibration problems. Zbl 0994.74081Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 1 2000 The method of fundamental solutions for axisymmetric potential problems. Zbl 0932.74078Karageorghis, Andreas; Fairweather, Graeme 30 1999 The method of fundamental solutions for elliptic boundary value problems. Zbl 0922.65074Fairweather, Graeme; Karageorghis, Andreas 420 1998 Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. Zbl 0911.65095Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 19 1998 Orthogonal spline collocation methods for biharmonic problems. Zbl 0908.65103Lou, Zhou-Ming; Bialecki, Bernard; Fairweather, Graeme 10 1998 Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Zbl 0868.65068Fairweather, G.; López-Marcos, J. C. 25 1996 Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems. Zbl 0820.65009Bialecki, Bernard; Fairweather, Graeme 10 1995 Orthogonal spline collocation methods for Schrödinger-type equations in one space variable. Zbl 0806.65123Robinson, Mark P.; Fairweather, Graeme 33 1994 Spline collocation methods for a class of hyperbolic partial integro- differential equations. Zbl 0814.65137Fairweather, Graeme 22 1994 An explicit extrapolated box scheme for the Gurtin-MacCamy equation. Zbl 0792.65108Fairweather, G.; López-Marcos, J. C. 7 1994 Fourier methods for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0805.65107Bialecki, Bernard; Fairweather, G.; Remington, K. A. 6 1994 An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G. 4 1994 Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. Zbl 0781.65031Bialecki, Bernard; Fairweather, Graeme 18 1993 Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0768.65067Fernandes, Ryan I.; Fairweather, Graeme 18 1993 A fourth-order cubic spline method for linear second-order two-point boundary-value problems. Zbl 0790.65078Sloan, Ian H.; Tran, Dat; Fairweather, Graeme 7 1993 On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112Robinson, M. P.; Fairweather, G.; Herbst, B. M. 6 1993 Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems. Zbl 1360.76291Robinson, Mark P.; Fairweather, Graeme 4 1993 Direct numerical spline methods for first-order Fredholm integro- differential equations. Zbl 0799.65153Micula, Gheorghe; Fairweather, Graeme 2 1993 Orthogonal spline collocation methods for some partial integrodifferential equations. Zbl 0756.65157Yan, Yi; Fairweather, Graeme 32 1992 Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations. Zbl 0752.65076Bialecki, Bernard; Fairweather, Graeme; Bennett, Karin R. 21 1992 The method of fundamental solutions for transmission and scattering of elastic waves. Zbl 0825.73150Kondapalli, Prasanna S.; Shippy, Davdi J.; Fairweather, Graeme 12 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 0892.65051Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 10 1992 The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65050Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 9 1992 The reformulation and numerical solution of certain nonclassical initial- boundary value problems. Zbl 0722.65062Fairweather, Graeme; Saylor, Rick D. 33 1991 A box method for a nonlinear equation of population dynamics. Zbl 0734.92023Fairweather, G.; López-Marcos, J. C. 15 1991 An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables. Zbl 0747.65082Fernandes, Ryan I.; Fairweather, Graeme 14 1991 Galerkin and collocation methods for partial integro-differential equations. Zbl 0737.65103Fairweather, G. 8 1991 Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. Zbl 0722.76073Shippy, D. J.; Kondapalli, P. S.; Fairweather, G. 10 1990 The simple layer potential method of fundamental solutions for certain biharmonic problems. Zbl 0687.76028Karageorghis, Andreas; Fairweather, Graeme 21 1989 The method of fundamental solutions for the solution of nonlinear plane potential problems. Zbl 0676.65110Karageorghis, A.; Fairweather, G. 21 1989 Finite element methods for nonlinear parabolic and hyperbolic partial integro-differential equations. Zbl 0726.65160Fairweather, Graeme; Yanik, Elizabeth G. 2 1989 A survey of spline collocation methods for the numerical solution of differential equations. Zbl 0679.65058Fairweather, Graeme; Maede, Daniel 2 1989 Finite element methods for parabolic and hyperbolic partial integro- differential equations. Zbl 0657.65142Yanik, Elizabeth G.; Fairweather, Graeme 69 1988 The Almansi method of fundamental solutions for solving biharmonic problems. Zbl 0639.65066Karageorghis, Andreas; Fairweather, Graeme 21 1988 Remark on algorithm 603. Zbl 0645.65017Diaz, J. C.; Fairweather, G.; Keast, P. 1 1988 The method of fundamental solutions for the numerical solution of the biharmonic equation. Zbl 0618.65108Karageorghis, Andreas; Fairweather, Graeme 98 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 0611.00023Keast, Patrick (ed.); Fairweather, Graeme (ed.) 3 1987 An assessment of numerical software for solving two-point boundary-value problems arising in heat transfer. Zbl 0619.76046Fairweather, Graeme; Vedha-Nayagam, M. 1 1987 Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0595.65122Greenwell-Yanik, C. E.; Fairweather, G. 25 1986 The method of fundamental solutions for problems in potential flow. Zbl 0546.76021Johnston, R. L.; Fairweather, G. 34 1984 A survey of higher-order methods for the numerical integration of semidiscrete parabolic problems. Zbl 0561.65087Seward, W. L.; Fairweather, G.; Johnston, R. L. 8 1984 On the \(H^{-1}\)-Galerkin method for second-order linear two-point boundary value problems. Zbl 0546.65056Fairweather, Graeme; Keast, Patrick; Diaz, Julio Cesar 1 1984 FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. Zbl 0516.65013Diaz, J. C.; Fairweather, G.; Keast, P. 38 1983 On the application of extrapolation, deferred correction and defect correction to discrete-time Galerkin methods for parabolic problems. Zbl 0573.65086Fairweather, G.; Saylor, A. V. 1 1983 The method of fundamental solutions for problems in potential theory. Zbl 0511.65087Fairweather, Graeme; Johnston, R. L. 12 1982 A linear ADI method for the shallow-water equations. Zbl 0454.76032Fairweather, G.; Navon, I. M. 3 1980 On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method. Zbl 0397.65080Fairweather, Graeme; Rizzo, Frank J.; Shippy, David J.; Wu, Yensen S. 15 1979 On the approximate solution of a diffusion problem by Galerkin methods. Zbl 0428.65062Fairweather, G. 2 1979 Finite element Galerkin methods for differential equations. Zbl 0372.65044Fairweather, Graeme 66 1978 A note on the efficient implementation of certain Padé methods for linear parabolic problems. Zbl 0384.65036Fairweather, Graeme 10 1978 An investigation of Romberg quadrature. Zbl 0394.65008Fairweather, Graeme; Keast, Pat 2 1978 Errata: Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0331.65078Dendy, J. E. jun.; Fairweather, G. 1 1976 Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0295.65062Dendy, J. E. jun.; Fairweather, G. 18 1975 On the extrapolation of Galerkin methods for parabolic problems. Zbl 0282.65080Fairweather, G.; Johnson, J. P. 2 1975 Three-level Galerkin methods for parabolic equations. Zbl 0313.65107Dupont, Todd; Fairweather, Graeme; Johnson, J. Peter 33 1974 Galerkin method for vibration problems in two space variables. Zbl 0246.65031Fairweather, Graeme 8 1972 A survey of discrete Galerkin methods for parabolic equations in one space variable. Zbl 0249.65068Fairweather, Graeme 1 1972 On the eigenvalues and eigenvectors of a class of Hessenberg matrices. Zbl 0217.52603Fairweather, G. 9 1971 Corrigenda. ’Some stable difference approximations to a fourth-order parabolic partial differential equation’, Math. Comp., v. 21, 1967, pp. 1-11. Zbl 0153.46405Fairweather, G.; Gourlay, A. R. 4 1968 A new computational procedure for A.D.I. methods. Zbl 0252.65072Fairweather, G.; Mitchell, A. R. 40 1967 Some stable difference approximations to a fourth-order parabolic partial differential equation. Zbl 0147.13801Fairweather, G.; Gourlay, A. R. 14 1967 Some high accuracy difference with a Splitting operator for equations of parabolic and elliptic type. Zbl 0148.39403Fairweather, G.; Gourlay, A. R.; Mitchell, A. R. 11 1967 Some computational results of an improved A. D. I. method for the Dirichlet problem. Zbl 0148.39404Fairweather, G.; Mitchell, A. R. 1 1966 A high accuracy alternating direction method for the wave equation. Zbl 0221.65180Fairweather, G.; Mitchell, A. R. 18 1965 A new alternating direction method for parabolic equations in three space variables. Zbl 0137.33302Fairweather, G.; Mitchell, A. R. 5 1965 Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations. Zbl 0123.12001Mitchell, A. R.; Fairweather, G. 23 1964 all cited Publications top 5 cited Publications 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 all top 5 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. 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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 all top 5 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) Citations by Year