# zbMATH — the first resource for mathematics

## Butcher, John C.

Compute Distance To:
 Author ID: butcher.john-c Published as: Butcher, J. C.; Butcher, John; Butcher, John C. Homepage: https://www.math.auckland.ac.nz/~butcher/ External Links: MGP · Wikidata · ORCID · ResearchGate · dblp · GND
 Documents Indexed: 163 Publications since 1956, including 8 Books Reviewing Activity: 43 Reviews Biographic References: 2 Publications
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#### Co-Authors

 95 single-authored 14 Jackiewicz, Zdzislaw 5 Cash, Jeff R. 5 Chartier, Philippe 4 Chan, T. M. H. 3 Burrage, Kevin 3 Chen, D. J. L. 3 Hill, Adrian T. 3 Imran, Gulshad 3 Podhaisky, Helmut 3 Wright, Will M. 2 Abdi, Ali 2 Chan, Robert Peng Kong 2 Chipman, F. H. 2 Diamantakis, M. T. 2 Norton, Terence J. T. 2 van der Houwen, Pieter J. 1 Ahmad, Saghir 1 Cooper, Gavin J. 1 Corless, Robert Malcolm 1 D’Ambrosio, Raffaele 1 Elhay, Sylvan 1 Enright, Wayne H. 1 Gonzalez-Vega, Laureano 1 Habib, Yousaf 1 Heard, A. D. 1 Hewitt, L. L. 1 Hojjati, Gholamreza 1 Johnston, P. B. 1 Kautsky, Jaroslav 1 Mazzia, Francesca 1 Messel, Harry 1 Mittelmann, Hans Detlef 1 Miyatake, Yuto 1 Moir, Nicolette 1 Moore, Gerald 1 O’Sullivan, A. E. 1 Rabinowitz, Philip 1 Rattenbury, Nicolette 1 Russell, Robert D. 1 Sanz-Serna, Jesús María 1 Sehnalová, Pavla 1 Shakoori, Azar 1 Singh, Adit D. 1 Söderling, G. 1 Sweatman, Winston L. 1 Tracogna, S. 1 Wanner, Gerhard 1 Weiner, Rüdiger 1 Wright, William M.
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#### Serials

 27 Applied Numerical Mathematics 24 Numerical Algorithms 22 BIT 10 Mathematics of Computation 7 SIAM Journal on Numerical Analysis 5 Journal of Computational and Applied Mathematics 5 BIT. Nordisk Tidskrift for Informationsbehandling 3 IMA Journal of Numerical Analysis 3 Computing 3 Journal of the Association for Computing Machinery 3 Journal of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 ACM Transactions on Mathematical Software 2 Numerische Mathematik 2 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 Biometrika 1 Bulletin of the London Mathematical Society 1 The Computer Journal. Section A / Section B 1 The Fibonacci Quarterly 1 Mathematics and Computers in Simulation 1 Journal of Complexity 1 Journal of Scientific Computing 1 Linear Algebra and its Applications 1 Bulletin. The Institute of Mathematics and its Applications 1 The Canadian Applied Mathematics Quarterly 1 Computational and Applied Mathematics 1 Advances in Computational Mathematics 1 The Arabian Journal for Science and Engineering. Section C: Theme Issues 1 The ANZIAM Journal 1 Acta Numerica 1 Nuclear Physics 1 Axioms
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#### Fields

 145 Numerical analysis (65-XX) 102 Ordinary differential equations (34-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 General and overarching topics; collections (00-XX) 6 History and biography (01-XX) 3 Combinatorics (05-XX) 3 Approximations and expansions (41-XX) 2 Number theory (11-XX) 2 Mechanics of particles and systems (70-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH

138 Publications have been cited 3,551 times in 1,911 Documents Cited by Year
The numerical analysis of ordinary differential equations. Runge-Kutta and general linear methods. Zbl 0616.65072
Butcher, J. C.
1987
Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041
Butcher, J. C.
2008
Implicit Runge-Kutta processes. Zbl 0123.11701
Butcher, J. C.
1964
Numerical methods for ordinary differential equations. Zbl 1040.65057
Butcher, J. C.
2003
Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043
Burrage, Kevin; Butcher, J. C.
1979
Coefficients for the study of Runge-Kutta integration processes. Zbl 0223.65031
Butcher, J. C.
1963
Non-linear stability of a general class of differential equation methods. Zbl 0431.65051
Burrage, Kevin; Butcher, J. C.
1980
An algebraic theory of integration methods. Zbl 0258.65070
Butcher, J. C.
1972
On the implementation of implicit Runge-Kutta methods. Zbl 0336.65037
Butcher, J. C.
1976
Some numerical methods for stiff problems. Zbl 1032.65512
Butcher, J. C.
2003
On Runge-Kutta processes of high order. Zbl 0244.65046
Butcher, J. C.
1964
Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004
Butcher, J. C.
2016
Diagonally-implicit multi-stage integration methods. Zbl 0773.65046
Butcher, J. C.
1993
On the convergence of numerical solutions to ordinary differential equations. Zbl 0141.13504
Butcher, J. C.
1966
A stability property of implicit Runge-Kutta methods. Zbl 0333.65031
Butcher, J. C.
1975
An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040
Burrage, K.; Butcher, J. C.; Chipman, F. H.
1980
The order of numerical methods for ordinary differential equations. Zbl 0278.65073
Butcher, J. C.
1973
General linear methods. Zbl 1113.65072
Butcher, J. C.
2006
Butcher, J. C.
1964
Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043
Butcher, J. C.; Jackiewicz, Z.
1993
A modified multistep method for the numerical integration of ordinary differential equations. Zbl 0125.07102
Butcher, J. C.
1965
Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044
Butcher, J. C.; Jackiewicz, Z.
1997
Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations. Zbl 0865.65056
Butcher, J. C.; Jackiewicz, Z.
1996
The construction of practical general linear methods. Zbl 1046.65054
Butcher, J. C.; Wright, W. M.
2003
Second derivative methods with RK stability. Zbl 1084.65069
Butcher, J. C.; Hojjati, G.
2005
Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080
Butcher, J. C.; Jackiewicz, Z.
1998
An iteration scheme for implicit Runge-Kutta methods. Zbl 0525.65052
Cooper, G. J.; Butcher, J. C.
1983
A transformed implicit Runge-Kutta method. Zbl 0439.65057
Butcher, J. C.
1979
On the attainable order of Runge-Kutta methods. Zbl 0132.36401
Butcher, J. C.
1965
The effective order of Runge-Kutta methods. Zbl 0185.41301
Butcher, J. C.
1969
Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077
Butcher, J. C.; Tracogna, S.
1997
Trees and numerical methods for ordinary differential equations. Zbl 1184.65072
Butcher, J. C.
2010
Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063
Butcher, J. C.
2000
General linear methods for stiff differential equations. Zbl 0983.65085
Butcher, J. C.
2001
A history of Runge-Kutta methods. Zbl 0858.65073
Butcher, J. C.
1996
The control of parasitism in $$G$$-symplectic methods. Zbl 1309.65148
Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T.
2014
Nordsieck representation of DIMSIMs. Zbl 0920.65043
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
1997
Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068
Butcher, J. C.; Jackiewicz, Z.; Wright, W. M.
2007
Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083
Butcher, J. C.; Jackiewicz, Z.
2004
A new approach to error estimation for general linear methods. Zbl 1032.65088
Butcher, J. C.; Jackiewicz, Z.
2003
Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
1999
ARK methods for stiff problems. Zbl 1070.65059
Butcher, John C.; Rattenbury, Nicolette
2005
Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072
Butcher, J. C.; Cash, J. R.
1990
The equivalence of algebraic stability and AN-stability. Zbl 0637.65083
Butcher, J. C.
1987
Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078
Butcher, J. C.; Jackiewicz, Z.
2004
A multistep generalization of Runge-Kutta methods with four or five stages. Zbl 0168.13901
Butcher, J. C.
1967
The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089
Butcher, J. C.; Chartier, P.
1999
A nonlinear optimization approach to the construction of general linear methods of high order. Zbl 0879.65051
Butcher, J. C.; Jackiewicz, Z.; Mittelmann, H. D.
1997
On A-stable implicit Runge-Kutta methods. Zbl 0378.65039
Butcher, J. C.
1977
A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232
Miyatake, Yuto; Butcher, John C.
2016
A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058
Butcher, J. C.; Chen, D. J. L.
2000
DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064
Butcher, J. C.; Diamantakis, M. T.
1998
DESI methods for stiff initial-value problems. Zbl 0884.65077
Butcher, J. C.; Cash, J. R.; Diamantakis, M. T.
1996
On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080
Butcher, J. C.; Podhaisky, H.
2006
A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081
Butcher, J. C.; Jackiewicz, Z.
2001
A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076
Butcher, J. C.; Chartier, P.
1997
An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085
Butcher, J. C.
1997
Runge-Kutta methods: Some historical notes. Zbl 0867.65038
Butcher, J. C.; Wanner, G.
1996
The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040
Butcher, J. C.
1992
Towards efficient implementation of singly-implicit methods. Zbl 0639.65041
Butcher, J. C.
1988
Linear and non-linear stability for general linear methods. Zbl 0623.65074
Butcher, J. C.
1987
A generalization of singly-implicit methods. Zbl 0484.65048
Butcher, J. C.
1981
Trees, B-series and exponential integrators. Zbl 1185.65121
Butcher, J. C.
2010
The existence of symplectic general linear methods. Zbl 1176.65080
Butcher, J. C.; Hewitt, L. L.
2009
Order and stability of generalized Padé approximations. Zbl 1182.65111
Butcher, J. C.
2009
A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048
Butcher, J. C.; Wright, W. M.
2003
The non-existence of ten stage eighth order explicit Runge-Kutta methods. Zbl 0579.65066
Butcher, J. C.
1985
Order bounds for second derivative approximations. Zbl 1247.65103
Abdi, A.; Butcher, J. C.
2012
High order A-stable numerical methods for stiff problems. Zbl 1203.65106
Butcher, J. C.
2005
Stability of numerical methods for ordinary differential equations. Zbl 1016.65059
Butcher, J. C.; Heard, A. D.
2002
The $$A$$-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057
Butcher, J. C.
2002
General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059
Butcher, J. C.
1993
The adaptation of STRIDE to delay differential equations. Zbl 0776.65049
Butcher, J. C.
1992
General linear method: A survey. Zbl 0619.65057
Butcher, J. C.
1985
Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272
Butcher, John C.; D’Ambrosio, Raffaele
2017
Thirty years of G-stability. Zbl 1105.65085
Butcher, J. C.
2006
Linear multistep methods as irreducible general linear methods. Zbl 1102.65078
Butcher, J. C.; Hill, A. T.
2006
Applications of doubly companion matrices. Zbl 1089.65065
Butcher, J. C.; Wright, W. M.
2006
Error estimation for Nordsieck methods. Zbl 1012.65083
Butcher, J. C.; Jackiewicz, Z.
2002
General linear methods. Zbl 0874.65057
Butcher, J. C.
1996
The number of conditions for a Runge-Kutta method to have effective order $$p$$. Zbl 0867.65039
Butcher, J. C.; Sanz-Serna, J. M.
1996
A transformation for the analysis of DIMSIMs. Zbl 0814.65079
Butcher, J. C.
1994
Some implementation schemes for implicit Runge-Kutta methods. Zbl 0447.65042
Butcher, J. C.
1980
On the integration processes of A. Huta. Zbl 0223.65032
Butcher, J. C.
1963
Symmetric general linear methods. Zbl 1355.65095
Butcher, J. C.; Hill, A. T.; Norton, T. J. T.
2016
Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068
Butcher, J. C.
2013
On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119
Butcher, J. C.
2009
Generalized Padé approximations to the exponential function. Zbl 0789.65063
Butcher, J. C.; Chipman, F. H.
1992
On sequences of imbedded integration rules. Zbl 0635.41024
Rabinowitz, Philip; Kautsky, Jaroslav; Elhay, Sylvan; Butcher, John C.
1987
An application of the Runge-Kutta space. Zbl 0555.65045
Butcher, J. C.
1984
Random sampling from the normal distribution. Zbl 0094.13503
Butcher, J. C.
1961
Applications of order arrows. Zbl 1241.65070
Abdi, A.; Butcher, J. C.
2012
Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002
Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar
2011
Forty-five years of A-stability. Zbl 1191.65109
Butcher, J. C.
2009
Order and effective order. Zbl 0927.65095
Butcher, J. C.
1998
Efficient Runge-Kutta integrators for index-2 differential algebraic equations. Zbl 0899.65048
Butcher, J. C.; Chan, R. P. K.
1998
Defect correction for two-point boundary value problems on nonequidistant meshes. Zbl 0828.65102
Butcher, J. C.; Cash, J. R.; Moore, G.; Russell, R. D.
1995
Optimal order and stepsize sequences. Zbl 0615.65076
Butcher, J. C.
1986
An order bound for Runge-Kutta methods. Zbl 0318.65030
Butcher, J. C.
1975
Symplectic effective order methods. Zbl 1291.65359
2014
Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272
Butcher, John C.; D’Ambrosio, Raffaele
2017
A G-symplectic method with order 6. Zbl 1367.65190
Butcher, John C.; Imran, Gulshad; Podhaisky, Helmut
2017
Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004
Butcher, J. C.
2016
A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232
Miyatake, Yuto; Butcher, John C.
2016
Symmetric general linear methods. Zbl 1355.65095
Butcher, J. C.; Hill, A. T.; Norton, T. J. T.
2016
Order conditions for G-symplectic methods. Zbl 1338.65185
2015
The cohesiveness of G-symplectic methods. Zbl 1330.65192
Butcher, J. C.
2015
Runge-Kutta methods for ordinary differential equations. Zbl 1330.65109
Butcher, J. C.
2015
The control of parasitism in $$G$$-symplectic methods. Zbl 1309.65148
Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T.
2014
Symplectic effective order methods. Zbl 1291.65359
2014
Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068
Butcher, J. C.
2013
Predictor-corrector Obreshkov pairs. Zbl 1307.65099
Butcher, John C.; Sehnalová, Pavla
2013
Order bounds for second derivative approximations. Zbl 1247.65103
Abdi, A.; Butcher, J. C.
2012
Applications of order arrows. Zbl 1241.65070
Abdi, A.; Butcher, J. C.
2012
Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002
Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar
2011
Trees and numerical methods for ordinary differential equations. Zbl 1184.65072
Butcher, J. C.
2010
Trees, B-series and exponential integrators. Zbl 1185.65121
Butcher, J. C.
2010
The tree and forest spaces with applications to initial-value problem methods. Zbl 1205.65211
Butcher, J. C.; Chan, T. M. H.
2010
B-series and B-series coefficients. Zbl 1432.65096
Butcher, J. C.
2010
The existence of symplectic general linear methods. Zbl 1176.65080
Butcher, J. C.; Hewitt, L. L.
2009
Order and stability of generalized Padé approximations. Zbl 1182.65111
Butcher, J. C.
2009
On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119
Butcher, J. C.
2009
Forty-five years of A-stability. Zbl 1191.65109
Butcher, J. C.
2009
General linear methods for ordinary differential equations. Zbl 1159.65333
Butcher, John
2009
Practical Runge-Kutta methods for scientific computation. Zbl 1178.65083
Butcher, J. C.
2009
Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041
Butcher, J. C.
2008
Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068
Butcher, J. C.; Jackiewicz, Z.; Wright, W. M.
2007
General linear methods. Zbl 1113.65072
Butcher, J. C.
2006
On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080
Butcher, J. C.; Podhaisky, H.
2006
Thirty years of G-stability. Zbl 1105.65085
Butcher, J. C.
2006
Linear multistep methods as irreducible general linear methods. Zbl 1102.65078
Butcher, J. C.; Hill, A. T.
2006
Applications of doubly companion matrices. Zbl 1089.65065
Butcher, J. C.; Wright, W. M.
2006
Second derivative methods with RK stability. Zbl 1084.65069
Butcher, J. C.; Hojjati, G.
2005
ARK methods for stiff problems. Zbl 1070.65059
Butcher, John C.; Rattenbury, Nicolette
2005
High order A-stable numerical methods for stiff problems. Zbl 1203.65106
Butcher, J. C.
2005
Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083
Butcher, J. C.; Jackiewicz, Z.
2004
Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078
Butcher, J. C.; Jackiewicz, Z.
2004
Numerical methods for ordinary differential equations. Zbl 1040.65057
Butcher, J. C.
2003
Some numerical methods for stiff problems. Zbl 1032.65512
Butcher, J. C.
2003
The construction of practical general linear methods. Zbl 1046.65054
Butcher, J. C.; Wright, W. M.
2003
A new approach to error estimation for general linear methods. Zbl 1032.65088
Butcher, J. C.; Jackiewicz, Z.
2003
A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048
Butcher, J. C.; Wright, W. M.
2003
Experiments with a new fifth order method. Zbl 1030.65081
Butcher, John C.; Moir, Nicolette
2003
Stability of numerical methods for ordinary differential equations. Zbl 1016.65059
Butcher, J. C.; Heard, A. D.
2002
The $$A$$-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057
Butcher, J. C.
2002
Error estimation for Nordsieck methods. Zbl 1012.65083
Butcher, J. C.; Jackiewicz, Z.
2002
A new approach to the algebraic structures for integration methods. Zbl 1016.65047
Butcher, J. C.; Chan, T. M. H.
2002
Nordsieck methods with an off-step point. Zbl 1012.65074
Butcher, J. C.; O’Sullivan, A. E.
2002
Special issue: Numerical methods for ordinary differential equations (ANODE 2001), Auckland, New Zealand, January 8–12, 2001. Selected papers. Zbl 1017.00022
Butcher, J. C. (ed.); Enright, W. H. (ed.); Mazzia, F. (ed.); Söderling, G. (ed.); van der Houwen, P. J. (ed.)
2002
General linear methods for stiff differential equations. Zbl 0983.65085
Butcher, J. C.
2001
A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081
Butcher, J. C.; Jackiewicz, Z.
2001
On the implementation of ESIRK methods for stiff IVPs. Zbl 0974.65075
Butcher, J. C.; Chen, D. J. L.
2001
Variable stepsize schemes for effective order methods and enhanced order composition methods. Zbl 0976.65067
Butcher, J. C.; Chan, T. M. H.
2001
Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063
Butcher, J. C.
2000
A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058
Butcher, J. C.; Chen, D. J. L.
2000
Multi-step zero approximations for stepsize control. Zbl 0951.65072
Butcher, J. C.; Chan, T. M. H.
2000
The choice of parameters in parallel general linear methods for stiff problems. Zbl 0949.65076
Butcher, J. C.; Singh, A. D.
2000
Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
1999
The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089
Butcher, J. C.; Chartier, P.
1999
Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080
Butcher, J. C.; Jackiewicz, Z.
1998
DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064
Butcher, J. C.; Diamantakis, M. T.
1998
Order and effective order. Zbl 0927.65095
Butcher, J. C.
1998
Efficient Runge-Kutta integrators for index-2 differential algebraic equations. Zbl 0899.65048
Butcher, J. C.; Chan, R. P. K.
1998
ESIRK methods and variable stepsize. Zbl 0927.65096
Butcher, J. C.; Chen, D. J. L.
1998
ARK methods up to order five. Zbl 0907.65069
Butcher, J. C.
1998
Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044
Butcher, J. C.; Jackiewicz, Z.
1997
Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077
Butcher, J. C.; Tracogna, S.
1997
Nordsieck representation of DIMSIMs. Zbl 0920.65043
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
1997
A nonlinear optimization approach to the construction of general linear methods of high order. Zbl 0879.65051
Butcher, J. C.; Jackiewicz, Z.; Mittelmann, H. D.
1997
A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076
Butcher, J. C.; Chartier, P.
1997
An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085
Butcher, J. C.
1997
Order and stability of parallel methods for stiff problems. Zbl 0884.65090
Butcher, J. C.
1997
Numerical methods for differential equations and applications. Zbl 0912.65064
Butcher, J. C.
1997
Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations. Zbl 0865.65056
Butcher, J. C.; Jackiewicz, Z.
1996
A history of Runge-Kutta methods. Zbl 0858.65073
Butcher, J. C.
1996
DESI methods for stiff initial-value problems. Zbl 0884.65077
Butcher, J. C.; Cash, J. R.; Diamantakis, M. T.
1996
Runge-Kutta methods: Some historical notes. Zbl 0867.65038
Butcher, J. C.; Wanner, G.
1996
General linear methods. Zbl 0874.65057
Butcher, J. C.
1996
The number of conditions for a Runge-Kutta method to have effective order $$p$$. Zbl 0867.65039
Butcher, J. C.; Sanz-Serna, J. M.
1996
Defect correction for two-point boundary value problems on nonequidistant meshes. Zbl 0828.65102
Butcher, J. C.; Cash, J. R.; Moore, G.; Russell, R. D.
1995
Parallel general linear methods for stiff ordinary differential and differential algebraic equations. Zbl 0833.65073
Butcher, J. C.; Chartier, P.
1995
On fifth order Runge-Kutta methods. Zbl 0837.65073
Butcher, J. C.
1995
An introduction to DIMSIMs. Zbl 0838.65078
Butcher, J. C.
1995
A transformation for the analysis of DIMSIMs. Zbl 0814.65079
Butcher, J. C.
1994
Initial value problems: Numerical methods and mathematics. Zbl 0817.65059
Butcher, J. C.
1994
Some orbital test problems. Zbl 0806.65068
Butcher, J. C.
1994
Diagonally-implicit multi-stage integration methods. Zbl 0773.65046
Butcher, J. C.
1993
Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043
Butcher, J. C.; Jackiewicz, Z.
1993
General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059
Butcher, J. C.
1993
The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040
Butcher, J. C.
1992
The adaptation of STRIDE to delay differential equations. Zbl 0776.65049
Butcher, J. C.
1992
Generalized Padé approximations to the exponential function. Zbl 0789.65063
Butcher, J. C.; Chipman, F. H.
1992
On symmetrizers for Gauss method. Zbl 0723.65045
Butcher, J. C.; Chan, R. P. K.
1992
Some new hybrid methods for initial value problems. Zbl 0769.65037
Butcher, J. C.
1992
Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072
Butcher, J. C.; Cash, J. R.
1990
Order, stepsize and stiffness switching. Zbl 0719.65059
Butcher, J. C.
1990
Towards efficient implementation of singly-implicit methods. Zbl 0639.65041
Butcher, J. C.
1988
On a class of matrices with real eigenvalues. Zbl 0667.15006
Butcher, J. C.
1988
The numerical analysis of ordinary differential equations. Runge-Kutta and general linear methods. Zbl 0616.65072
Butcher, J. C.
1987
The equivalence of algebraic stability and AN-stability. Zbl 0637.65083
Butcher, J. C.
1987
...and 38 more Documents
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#### Cited by 2,172 Authors

 75 Butcher, John C. 63 Jackiewicz, Zdzislaw 37 Weiner, Rüdiger 28 Tsitouras, Charalampos 27 D’Ambrosio, Raffaele 25 Abdi, Ali 23 Ismail, Fudziah Bt. 23 Kulikov, Gennady Yur’evich 21 Burrage, Kevin 21 Paternoster, Beatrice 20 Hairer, Ernst 19 Cash, Jeff R. 19 Senu, Norazak 19 You, Xiong 18 Hojjati, Gholamreza 18 Spijker, Marc N. 17 Podhaisky, Helmut 16 González-Pinto, Severiano 16 Sanz-Serna, Jesús María 16 Simos, Theodore E. 16 van der Houwen, Pieter J. 16 Wu, Xinyuan 15 Li, Shoufu 15 Montijano, Juan Ignacio 15 Schmitt, Bernhard A. 15 Zennaro, Marino 14 Cong, Nguyen Huu 14 Wanner, Gerhard 13 Brugnano, Luigi 13 Famelis, Ioannis Th. 13 Izzo, Giuseppe 13 Sommeijer, Ben P. 13 Zlatev, Zahari 12 Chartier, Philippe 12 Fang, Yonglei 12 Sandu, Adrian 12 Zhang, Chengjian 11 Chan, Robert Peng Kong 11 Cooper, Gavin J. 11 Hundsdorfer, Willem H. 11 Ketcheson, David I. 11 Rández, Luis 11 Van Daele, Marnix 10 Evans, David John 10 Ramos, Higinio 9 Calvo, Manuel 9 Hill, Adrian T. 9 Huang, Chengming 9 Li, Jiyong 9 Nørsett, Syvert Paul 9 Scherer, Rudolf 9 Vanden Berghe, Guido 9 Vermiglio, Rossana 9 Verner, James H. 9 Xiao, Aiguo 8 Blanes, Sergio 8 Cardone, Angelamaria 8 Debrabant, Kristian 8 Iavernaro, Felice 8 Kvaerno, Anne 8 Lubich, Christian 8 Magherini, Cecilia 8 Manchon, Dominique 8 Mitsui, Taketomo 8 Munthe-Kaas, Hans Z. 8 Schneid, Josef 8 Tian, Hongjiong 8 Wang, Wansheng 8 Wang, Zhongqing 8 Wen, Liping 8 Yu, Yuexin 7 Braś, Michał 7 Corless, Robert Malcolm 7 De Meyer, Hans E. 7 Dormand, John R. 7 Enright, Wayne H. 7 Gottlieb, Sigal 7 Ibrahim, Zarina Bibi Binti 7 Iserles, Arieh 7 Kraaijevanger, J. F. B. M. 7 Kulikova, Maria V. 7 Martín-Vaquero, Jesús 7 Murugesan, K. 7 Murugesh, V. 7 Nakashima, Masaharu 7 Ostermann, Alexander 7 Prince, P. J. 7 Tang, Wensheng 7 Vaillancourt, Rémi 7 Verwer, Jan G. 6 Axelsson, Axel Owe Holger 6 Bellen, Alfredo 6 Burrage, Pamela M. 6 Chen, Zhaoxia 6 Conte, Dajana 6 Ebrahimi-Fard, Kurusch 6 Faragó, István 6 Frank, Reinhard 6 Georgiev, Krassimir 6 Havasi, Ágnes ...and 2,072 more Authors
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#### Cited in 250 Serials

 240 Applied Numerical Mathematics 204 Journal of Computational and Applied Mathematics 127 BIT 117 Applied Mathematics and Computation 112 Journal of Computational Physics 83 Numerical Algorithms 68 Computers & Mathematics with Applications 51 Numerische Mathematik 49 Mathematics of Computation 47 International Journal of Computer Mathematics 40 Journal of Scientific Computing 39 Computing 34 BIT. Nordisk Tidskrift for Informationsbehandling 26 Computer Methods in Applied Mechanics and Engineering 23 Journal of Mathematical Chemistry 21 Computer Physics Communications 17 Computers and Fluids 16 SIAM Journal on Scientific Computing 15 Calcolo 15 SIAM Journal on Numerical Analysis 15 Applied Mathematical Modelling 14 Applied Mathematics Letters 13 Computational and Applied Mathematics 13 Mathematical Problems in Engineering 12 Mathematics and Computers in Simulation 12 Foundations of Computational Mathematics 11 Journal of Applied Mathematics and Computing 10 Japan Journal of Industrial and Applied Mathematics 10 Advances in Computational Mathematics 9 Mathematical and Computer Modelling 8 Discrete Dynamics in Nature and Society 7 Communications in Nonlinear Science and Numerical Simulation 7 Journal of Applied Mathematics 6 Chaos, Solitons and Fractals 6 Computational Mathematics and Mathematical Physics 6 Linear Algebra and its Applications 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Discrete and Continuous Dynamical Systems 6 Abstract and Applied Analysis 5 International Journal for Numerical Methods in Engineering 5 Publications of the Research Institute for Mathematical Sciences, Kyoto University 5 Physica D 5 Celestial Mechanics and Dynamical Astronomy 5 Chaos 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Journal of Theoretical Biology 5 Axioms 4 Journal of Mathematical Analysis and Applications 4 Physics Letters. A 4 Bulletin of the Iranian Mathematical Society 4 Journal of Difference Equations and Applications 4 Nonlinear Dynamics 4 International Journal of Modern Physics C 4 Discrete and Continuous Dynamical Systems. Series B 4 International Journal of Computational Methods 4 Mediterranean Journal of Mathematics 4 Advances in Difference Equations 4 Symmetry 4 Afrika Matematika 3 Acta Mechanica 3 Communications in Mathematical Physics 3 Journal of Mathematical Physics 3 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 3 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 3 Annals of the Institute of Statistical Mathematics 3 The Annals of Probability 3 Journal of Computer and System Sciences 3 Numerical Functional Analysis and Optimization 3 Acta Applicandae Mathematicae 3 The Annals of Applied Probability 3 Applications of Mathematics 3 Celestial Mechanics 3 Computers and Mathematics with Applications. Part A 3 Monte Carlo Methods and Applications 3 Optimization Methods & Software 3 Computational Methods in Applied Mathematics 3 Discrete and Continuous Dynamical Systems. Series S 3 Statistics and Computing 2 International Journal of Mathematical Education in Science and Technology 2 Indian Journal of Pure & Applied Mathematics 2 Information Processing Letters 2 Journal of Engineering Mathematics 2 Journal of the Franklin Institute 2 Mathematical Biosciences 2 Physics Reports 2 Ukrainian Mathematical Journal 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Bulletin of Mathematical Biology 2 Advances in Mathematics 2 Automatica 2 Journal of Algebra 2 Journal of Optimization Theory and Applications 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the Japan Academy. Series A 2 Results in Mathematics 2 Theoretical Computer Science 2 Circuits, Systems, and Signal Processing 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Journal of Symbolic Computation 2 Journal of Complexity ...and 150 more Serials
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#### Cited in 54 Fields

 1,664 Numerical analysis (65-XX) 842 Ordinary differential equations (34-XX) 218 Partial differential equations (35-XX) 129 Fluid mechanics (76-XX) 108 Dynamical systems and ergodic theory (37-XX) 80 Probability theory and stochastic processes (60-XX) 56 Biology and other natural sciences (92-XX) 51 Mechanics of particles and systems (70-XX) 48 Integral equations (45-XX) 42 Systems theory; control (93-XX) 37 Approximations and expansions (41-XX) 35 Computer science (68-XX) 35 Mechanics of deformable solids (74-XX) 33 Quantum theory (81-XX) 28 Combinatorics (05-XX) 22 Associative rings and algebras (16-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 21 Operations research, mathematical programming (90-XX) 15 Optics, electromagnetic theory (78-XX) 15 Statistical mechanics, structure of matter (82-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Classical thermodynamics, heat transfer (80-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Statistics (62-XX) 12 History and biography (01-XX) 12 Information and communication theory, circuits (94-XX) 11 Geophysics (86-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 Nonassociative rings and algebras (17-XX) 8 Real functions (26-XX) 8 Difference and functional equations (39-XX) 8 Operator theory (47-XX) 5 Number theory (11-XX) 5 Differential geometry (53-XX) 5 Astronomy and astrophysics (85-XX) 4 General and overarching topics; collections (00-XX) 4 Integral transforms, operational calculus (44-XX) 4 Relativity and gravitational theory (83-XX) 3 Category theory; homological algebra (18-XX) 3 Topological groups, Lie groups (22-XX) 3 Special functions (33-XX) 3 Functional analysis (46-XX) 2 Functions of a complex variable (30-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX)

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