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Author ID: butcher.john-c Recent zbMATH articles by "Butcher, John C."
Published as: Butcher, J. C.; Butcher, John C.; Butcher, John
Further Spellings: Butcher, John Charles
Homepage: https://www.math.auckland.ac.nz/~butcher/
External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef
Documents Indexed: 160 Publications since 1956, including 5 Books
6 Contributions as Editor · 2 Further Contributions
Reviewing Activity: 43 Reviews
Biographic References: 2 Publications
Co-Authors: 48 Co-Authors with 68 Joint Publications
938 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

146 Publications have been cited 4,501 times in 2,614 Documents Cited by Year
The numerical analysis of ordinary differential equations. Runge-Kutta and general linear methods. Zbl 0616.65072
Butcher, J. C.
627
1987
Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041
Butcher, J. C.
426
2008
Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004
Butcher, J. C.
274
2016
Implicit Runge-Kutta processes. Zbl 0123.11701
Butcher, J. C.
259
1964
Numerical methods for ordinary differential equations. Zbl 1040.65057
Butcher, J. C.
192
2003
Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043
Burrage, Kevin; Butcher, J. C.
141
1979
An algebraic theory of integration methods. Zbl 0258.65070
Butcher, J. C.
139
1972
Coefficients for the study of Runge-Kutta integration processes. Zbl 0223.65031
Butcher, J. C.
132
1963
Non-linear stability of a general class of differential equation methods. Zbl 0431.65051
Burrage, Kevin; Butcher, J. C.
121
1980
On Runge-Kutta processes of high order. Zbl 0244.65046
Butcher, J. C.
112
1964
Modern numerical methods for ordinary differential equations. Zbl 0348.65064
109
1976
On the implementation of implicit Runge-Kutta methods. Zbl 0336.65037
Butcher, J. C.
104
1976
On the convergence of numerical solutions to ordinary differential equations. Zbl 0141.13504
Butcher, J. C.
83
1966
Diagonally-implicit multi-stage integration methods. Zbl 0773.65046
Butcher, J. C.
80
1993
Some numerical methods for stiff problems. Zbl 1032.65512
Butcher, J. C.
77
2003
A stability property of implicit Runge-Kutta methods. Zbl 0333.65031
Butcher, J. C.
70
1975
An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040
Burrage, K.; Butcher, J. C.; Chipman, F. H.
69
1980
General linear methods. Zbl 1113.65072
Butcher, J. C.
64
2006
Second derivative methods with RK stability. Zbl 1084.65069
Butcher, J. C.; Hojjati, G.
58
2005
The order of numerical methods for ordinary differential equations. Zbl 0278.65073
Butcher, J. C.
57
1973
Integration processes based on Radau quadrature formulas. Zbl 0123.11702
Butcher, J. C.
49
1964
A modified multistep method for the numerical integration of ordinary differential equations. Zbl 0125.07102
Butcher, J. C.
49
1965
Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043
Butcher, J. C.; Jackiewicz, Z.
49
1993
The construction of practical general linear methods. Zbl 1046.65054
Butcher, J. C.; Wright, W. M.
46
2003
Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044
Butcher, J. C.; Jackiewicz, Z.
42
1997
Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080
Butcher, J. C.; Jackiewicz, Z.
39
1998
Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations. Zbl 0865.65056
Butcher, J. C.; Jackiewicz, Z.
37
1996
The effective order of Runge-Kutta methods. Zbl 0185.41301
Butcher, J. C.
35
1969
An iteration scheme for implicit Runge-Kutta methods. Zbl 0525.65052
Cooper, G. J.; Butcher, J. C.
35
1983
A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232
Miyatake, Yuto; Butcher, John C.
33
2016
A transformed implicit Runge-Kutta method. Zbl 0439.65057
Butcher, J. C.
31
1979
Trees and numerical methods for ordinary differential equations. Zbl 1184.65072
Butcher, J. C.
29
2010
Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063
Butcher, J. C.
29
2000
On the attainable order of Runge-Kutta methods. Zbl 0132.36401
Butcher, J. C.
28
1965
A history of Runge-Kutta methods. Zbl 0858.65073
Butcher, J. C.
27
1996
Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077
Butcher, J. C.; Tracogna, S.
25
1997
The control of parasitism in \(G\)-symplectic methods. Zbl 1309.65148
Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T.
24
2014
Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
23
1999
Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083
Butcher, J. C.; Jackiewicz, Z.
22
2004
A multistep generalization of Runge-Kutta methods with four or five stages. Zbl 0168.13901
Butcher, J. C.
21
1967
General linear methods for stiff differential equations. Zbl 0983.65085
Butcher, J. C.
20
2001
Nordsieck representation of DIMSIMs. Zbl 0920.65043
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
19
1997
A new approach to error estimation for general linear methods. Zbl 1032.65088
Butcher, J. C.; Jackiewicz, Z.
16
2003
Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068
Butcher, J. C.; Jackiewicz, Z.; Wright, W. M.
16
2007
A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058
Butcher, J. C.; Chen, D. J. L.
16
2000
Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078
Butcher, J. C.; Jackiewicz, Z.
15
2004
ARK methods for stiff problems. Zbl 1070.65059
Butcher, John C.; Rattenbury, Nicolette
15
2005
The equivalence of algebraic stability and AN-stability. Zbl 0637.65083
Butcher, J. C.
15
1987
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.
15
1997
Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072
Butcher, J. C.; Cash, J. R.
14
1990
B-series. Algebraic analysis of numerical methods. Zbl 07332820
Butcher, John C.
14
2021
Trees, B-series and exponential integrators. Zbl 1185.65121
Butcher, J. C.
13
2010
Runge-Kutta methods: Some historical notes. Zbl 0867.65038
Butcher, J. C.; Wanner, G.
13
1996
The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089
Butcher, J. C.; Chartier, P.
13
1999
DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064
Butcher, J. C.; Diamantakis, M. T.
13
1998
The existence of symplectic general linear methods. Zbl 1176.65080
Butcher, J. C.; Hewitt, L. L.
12
2009
On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080
Butcher, J. C.; Podhaisky, H.
12
2006
On A-stable implicit Runge-Kutta methods. Zbl 0378.65039
Butcher, J. C.
12
1977
Stability of numerical methods for ordinary differential equations. Zbl 1016.65059
Butcher, J. C.; Heard, A. D.
12
2002
DESI methods for stiff initial-value problems. Zbl 0884.65077
Butcher, J. C.; Cash, J. R.; Diamantakis, M. T.
12
1996
The non-existence of ten stage eighth order explicit Runge-Kutta methods. Zbl 0579.65066
Butcher, J. C.
11
1985
Order and stability of generalized Padé approximations. Zbl 1182.65111
Butcher, J. C.
11
2009
A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081
Butcher, J. C.; Jackiewicz, Z.
11
2001
Linear multistep methods as irreducible general linear methods. Zbl 1102.65078
Butcher, J. C.; Hill, A. T.
11
2006
Linear and non-linear stability for general linear methods. Zbl 0623.65074
Butcher, J. C.
11
1987
An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085
Butcher, J. C.
11
1997
General linear methods. Zbl 0874.65057
Butcher, J. C.
11
1996
A generalization of singly-implicit methods. Zbl 0484.65048
Butcher, J. C.
11
1981
Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272
Butcher, John C.; D’Ambrosio, Raffaele
11
2017
Order bounds for second derivative approximations. Zbl 1247.65103
Abdi, A.; Butcher, J. C.
10
2012
A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048
Butcher, J. C.; Wright, W. M.
10
2003
Towards efficient implementation of singly-implicit methods. Zbl 0639.65041
Butcher, J. C.
10
1988
The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039
Butcher, J. C.; Sanz-Serna, J. M.
10
1996
A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076
Butcher, J. C.; Chartier, P.
10
1997
The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040
Butcher, J. C.
10
1992
General linear method: A survey. Zbl 0619.65057
Butcher, J. C.
9
1985
The adaptation of STRIDE to delay differential equations. Zbl 0776.65049
Butcher, J. C.
9
1992
On the integration processes of A. Huta. Zbl 0223.65032
Butcher, J. C.
9
1963
Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068
Butcher, J. C.
9
2013
General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059
Butcher, J. C.
9
1993
Applications of doubly companion matrices. Zbl 1089.65065
Butcher, J. C.; Wright, W. M.
8
2006
Some implementation schemes for implicit Runge-Kutta methods. Zbl 0447.65042
Butcher, J. C.
8
1980
Thirty years of G-stability. Zbl 1105.65085
Butcher, J. C.
8
2006
The \(A\)-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057
Butcher, J. C.
8
2002
High order A-stable numerical methods for stiff problems. Zbl 1203.65106
Butcher, J. C.
8
2005
Symmetric general linear methods. Zbl 1355.65095
Butcher, J. C.; Hill, A. T.; Norton, T. J. T.
8
2016
Error estimation for Nordsieck methods. Zbl 1012.65083
Butcher, J. C.; Jackiewicz, Z.
7
2002
On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119
Butcher, J. C.
7
2009
A transformation for the analysis of DIMSIMs. Zbl 0814.65079
Butcher, J. C.
7
1994
Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002
Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar
7
2011
Generalized Padé approximations to the exponential function. Zbl 0789.65063
Butcher, J. C.; Chipman, F. H.
7
1992
Order and stability of parallel methods for stiff problems. Zbl 0884.65090
Butcher, J. C.
7
1997
Forty-five years of A-stability. Zbl 1191.65109
Butcher, J. C.
6
2009
Random sampling from the normal distribution. Zbl 0094.13503
Butcher, J. C.
6
1961
On sequences of imbedded integration rules. Zbl 0635.41024
Rabinowitz, Philip; Kautsky, Jaroslav; Elhay, Sylvan; Butcher, John C.
6
1987
The cohesiveness of G-symplectic methods. Zbl 1330.65192
Butcher, J. C.
5
2015
Practical Runge-Kutta methods for scientific computation. Zbl 1178.65083
Butcher, J. C.
5
2009
An application of the Runge-Kutta space. Zbl 0555.65045
Butcher, J. C.
5
1984
Optimal order and stepsize sequences. Zbl 0615.65076
Butcher, J. C.
5
1986
Order conditions for G-symplectic methods. Zbl 1338.65185
Butcher, John C.; Imran, Gulshad
5
2015
High-order linearly implicit schemes conserving quadratic invariants. Zbl 07705764
Sato, Shun; Miyatake, Yuto; Butcher, John C.
2
2023
Isomeric trees and the order of Runge-Kutta methods. Zbl 1492.65202
Butcher, John C.; Podhaisky, Helmut
1
2022
B-series. Algebraic analysis of numerical methods. Zbl 07332820
Butcher, John C.
14
2021
Trees, stumps, and applications. Zbl 1432.65087
Butcher, John C.
1
2018
Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272
Butcher, John C.; D’Ambrosio, Raffaele
11
2017
A G-symplectic method with order 6. Zbl 1367.65190
Butcher, John C.; Imran, Gulshad; Podhaisky, Helmut
4
2017
Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004
Butcher, J. C.
274
2016
A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232
Miyatake, Yuto; Butcher, John C.
33
2016
Symmetric general linear methods. Zbl 1355.65095
Butcher, J. C.; Hill, A. T.; Norton, T. J. T.
8
2016
The cohesiveness of G-symplectic methods. Zbl 1330.65192
Butcher, J. C.
5
2015
Order conditions for G-symplectic methods. Zbl 1338.65185
Butcher, John C.; Imran, Gulshad
5
2015
Runge-Kutta methods for ordinary differential equations. Zbl 1330.65109
Butcher, J. C.
4
2015
The control of parasitism in \(G\)-symplectic methods. Zbl 1309.65148
Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T.
24
2014
Symplectic effective order methods. Zbl 1291.65359
Butcher, John C.; Imran, Gulshad
4
2014
Walter Gautschi, Volume 3. Selected works with commentaries. Edited by Claude Brezinski and Ahmed Sameh. Zbl 1292.01007
Gautschi, Walter
1
2014
Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068
Butcher, J. C.
9
2013
Predictor-corrector Obreshkov pairs. Zbl 1307.65099
Butcher, John C.; Sehnalová, Pavla
4
2013
Order bounds for second derivative approximations. Zbl 1247.65103
Abdi, A.; Butcher, J. C.
10
2012
Applications of order arrows. Zbl 1241.65070
Abdi, A.; Butcher, J. C.
5
2012
Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002
Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar
7
2011
Trees and numerical methods for ordinary differential equations. Zbl 1184.65072
Butcher, J. C.
29
2010
Trees, B-series and exponential integrators. Zbl 1185.65121
Butcher, J. C.
13
2010
The tree and forest spaces with applications to initial-value problem methods. Zbl 1205.65211
Butcher, J. C.; Chan, T. M. H.
3
2010
B-series and B-series coefficients. Zbl 1432.65096
Butcher, J. C.
1
2010
The existence of symplectic general linear methods. Zbl 1176.65080
Butcher, J. C.; Hewitt, L. L.
12
2009
Order and stability of generalized Padé approximations. Zbl 1182.65111
Butcher, J. C.
11
2009
On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119
Butcher, J. C.
7
2009
Forty-five years of A-stability. Zbl 1191.65109
Butcher, J. C.
6
2009
Practical Runge-Kutta methods for scientific computation. Zbl 1178.65083
Butcher, J. C.
5
2009
General linear methods for ordinary differential equations. Zbl 1159.65333
Butcher, John
4
2009
Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041
Butcher, J. C.
426
2008
Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068
Butcher, J. C.; Jackiewicz, Z.; Wright, W. M.
16
2007
General linear methods. Zbl 1113.65072
Butcher, J. C.
64
2006
On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080
Butcher, J. C.; Podhaisky, H.
12
2006
Linear multistep methods as irreducible general linear methods. Zbl 1102.65078
Butcher, J. C.; Hill, A. T.
11
2006
Applications of doubly companion matrices. Zbl 1089.65065
Butcher, J. C.; Wright, W. M.
8
2006
Thirty years of G-stability. Zbl 1105.65085
Butcher, J. C.
8
2006
Second derivative methods with RK stability. Zbl 1084.65069
Butcher, J. C.; Hojjati, G.
58
2005
ARK methods for stiff problems. Zbl 1070.65059
Butcher, John C.; Rattenbury, Nicolette
15
2005
High order A-stable numerical methods for stiff problems. Zbl 1203.65106
Butcher, J. C.
8
2005
Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083
Butcher, J. C.; Jackiewicz, Z.
22
2004
Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078
Butcher, J. C.; Jackiewicz, Z.
15
2004
Numerical methods for ordinary differential equations. Zbl 1040.65057
Butcher, J. C.
192
2003
Some numerical methods for stiff problems. Zbl 1032.65512
Butcher, J. C.
77
2003
The construction of practical general linear methods. Zbl 1046.65054
Butcher, J. C.; Wright, W. M.
46
2003
A new approach to error estimation for general linear methods. Zbl 1032.65088
Butcher, J. C.; Jackiewicz, Z.
16
2003
A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048
Butcher, J. C.; Wright, W. M.
10
2003
Experiments with a new fifth order method. Zbl 1030.65081
Butcher, John C.; Moir, Nicolette
2
2003
Stability of numerical methods for ordinary differential equations. Zbl 1016.65059
Butcher, J. C.; Heard, A. D.
12
2002
The \(A\)-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057
Butcher, J. C.
8
2002
Error estimation for Nordsieck methods. Zbl 1012.65083
Butcher, J. C.; Jackiewicz, Z.
7
2002
A new approach to the algebraic structures for integration methods. Zbl 1016.65047
Butcher, J. C.; Chan, T. M. H.
4
2002
Nordsieck methods with an off-step point. Zbl 1012.65074
Butcher, J. C.; O’Sullivan, A. E.
2
2002
Special issue: Numerical methods for ordinary differential equations (ANODE 2001), Auckland, New Zealand, January 8–12, 2001. Selected papers. Zbl 1017.00022
1
2002
General linear methods for stiff differential equations. Zbl 0983.65085
Butcher, J. C.
20
2001
A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081
Butcher, J. C.; Jackiewicz, Z.
11
2001
On the implementation of ESIRK methods for stiff IVPs. Zbl 0974.65075
Butcher, J. C.; Chen, D. J. L.
4
2001
Variable stepsize schemes for effective order methods and enhanced order composition methods. Zbl 0976.65067
Butcher, J. C.; Chan, T. M. H.
2
2001
Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063
Butcher, J. C.
29
2000
A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058
Butcher, J. C.; Chen, D. J. L.
16
2000
The choice of parameters in parallel general linear methods for stiff problems. Zbl 0949.65076
Butcher, J. C.; Singh, A. D.
2
2000
Multi-step zero approximations for stepsize control. Zbl 0951.65072
Butcher, J. C.; Chan, T. M. H.
2
2000
Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
23
1999
The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089
Butcher, J. C.; Chartier, P.
13
1999
Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080
Butcher, J. C.; Jackiewicz, Z.
39
1998
DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064
Butcher, J. C.; Diamantakis, M. T.
13
1998
Order and effective order. Zbl 0927.65095
Butcher, J. C.
5
1998
Efficient Runge-Kutta integrators for index-2 differential algebraic equations. Zbl 0899.65048
Butcher, J. C.; Chan, R. P. K.
5
1998
ESIRK methods and variable stepsize. Zbl 0927.65096
Butcher, J. C.; Chen, D. J. L.
3
1998
ARK methods up to order five. Zbl 0907.65069
Butcher, J. C.
2
1998
Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044
Butcher, J. C.; Jackiewicz, Z.
42
1997
Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077
Butcher, J. C.; Tracogna, S.
25
1997
Nordsieck representation of DIMSIMs. Zbl 0920.65043
Butcher, J. C.; Chartier, P.; Jackiewicz, Z.
19
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.
15
1997
An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085
Butcher, J. C.
11
1997
A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076
Butcher, J. C.; Chartier, P.
10
1997
Order and stability of parallel methods for stiff problems. Zbl 0884.65090
Butcher, J. C.
7
1997
Numerical methods for differential equations and applications. Zbl 0912.65064
Butcher, J. C.
1
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.
37
1996
A history of Runge-Kutta methods. Zbl 0858.65073
Butcher, J. C.
27
1996
Runge-Kutta methods: Some historical notes. Zbl 0867.65038
Butcher, J. C.; Wanner, G.
13
1996
DESI methods for stiff initial-value problems. Zbl 0884.65077
Butcher, J. C.; Cash, J. R.; Diamantakis, M. T.
12
1996
General linear methods. Zbl 0874.65057
Butcher, J. C.
11
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.
10
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.
5
1995
Parallel general linear methods for stiff ordinary differential and differential algebraic equations. Zbl 0833.65073
Butcher, J. C.; Chartier, P.
5
1995
On fifth order Runge-Kutta methods. Zbl 0837.65073
Butcher, J. C.
3
1995
An introduction to DIMSIMs. Zbl 0838.65078
Butcher, J. C.
1
1995
A transformation for the analysis of DIMSIMs. Zbl 0814.65079
Butcher, J. C.
7
1994
Initial value problems: Numerical methods and mathematics. Zbl 0817.65059
Butcher, J. C.
2
1994
Some orbital test problems. Zbl 0806.65068
Butcher, J. C.
2
1994
Diagonally-implicit multi-stage integration methods. Zbl 0773.65046
Butcher, J. C.
80
1993
Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043
Butcher, J. C.; Jackiewicz, Z.
49
1993
General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059
Butcher, J. C.
9
1993
Estimating local truncation errors for Runge-Kutta methods. Zbl 0789.65066
Butcher, J. C.; Johnston, P. B.
2
1993
The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040
Butcher, J. C.
10
1992
The adaptation of STRIDE to delay differential equations. Zbl 0776.65049
Butcher, J. C.
9
1992
Generalized Padé approximations to the exponential function. Zbl 0789.65063
Butcher, J. C.; Chipman, F. H.
7
1992
On symmetrizers for Gauss method. Zbl 0723.65045
Butcher, J. C.; Chan, R. P. K.
3
1992
Some new hybrid methods for initial value problems. Zbl 0769.65037
Butcher, J. C.
2
1992
...and 46 more Documents
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Cited by 3,085 Authors

78 Butcher, John C.
76 Jackiewicz, Zdzislaw
50 Tsitouras, Charalampos
48 Abdi, Ali
42 Hojjati, Gholamreza
39 Simos, Theodore E.
37 Weiner, Rüdiger
36 D’Ambrosio, Raffaele
30 Paternoster, Beatrice
28 Kulikov, Gennady Yur’evich
28 Senu, Norazak
27 Ismail, Fudziah Bt.
23 Ramos, Higinio
22 Izzo, Giuseppe
21 Burrage, Kevin
21 You, Xiong
20 Hairer, Ernst
20 Podhaisky, Helmut
20 Sanz-Serna, Jesús María
19 Cash, Jeff R.
19 Montijano, Juan Ignacio
19 Spijker, Marc N.
18 González-Pinto, Severiano
17 Li, Shoufu
17 van der Houwen, Pieter J.
16 Famelis, Ioannis Th.
16 Sandu, Adrian
16 Wu, Xinyuan
15 Brugnano, Luigi
15 Ketcheson, David I.
15 Rández, Luis
15 Schmitt, Bernhard A.
15 Zennaro, Marino
14 Cong, Nguyen Huu
14 Conte, Dajana
14 Fang, Yonglei
14 Ikhile, Monday Ndidi Oziegbe
14 Li, Jiyong
14 Wanner, Gerhard
14 Zhang, Chengjian
14 Zlatev, Zahari
13 Calvo, Manuel
13 Sommeijer, Ben P.
12 Braś, Michał
12 Chartier, Philippe
12 Manchon, Dominique
12 Moradi, Afsaneh
12 Wang, Wansheng
11 Chan, Robert Peng Kong
11 Cooper, Gavin J.
11 Hundsdorfer, Willem H.
11 Munthe-Kaas, Hans Z.
11 Van Daele, Marnix
11 Xiao, Aiguo
10 Blanes, Sergio
10 Evans, David John
10 Gottlieb, Sigal
10 Huang, Chengming
10 Iavernaro, Felice
10 Verner, James H.
9 Cardone, Angelamaria
9 Corless, Robert Malcolm
9 Ebrahimi-Fard, Kurusch
9 Faragó, István
9 Hill, Adrian T.
9 Lubich, Christian
9 McLachlan, Robert I.
9 Nørsett, Syvert Paul
9 Ranocha, Hendrik
9 Scherer, Rudolf
9 Tian, Hongjiong
9 Vanden Berghe, Guido
9 Vermiglio, Rossana
9 Zhao, Weidong
8 Debrabant, Kristian
8 Havasi, Ágnes
8 Hernandez-Abreu, Domingo
8 Ibrahim, Zarina Bibi Binti
8 Kvaerno, Anne
8 Magherini, Cecilia
8 Mitsui, Taketomo
8 Miyatake, Yuto
8 Rufai, Mufutau Ajani
8 Schneid, Josef
8 Wang, Bin
8 Wang, Zhongqing
8 Wen, Liping
8 Yu, Yuexin
7 Axelsson, Axel Owe Holger
7 Bellen, Alfredo
7 Bruned, Yvain
7 Casas, Fernando
7 De Meyer, Hans E.
7 Dormand, John R.
7 Fazio, Riccardo
7 Georgiev, Krassimir
7 Iserles, Arieh
7 Koval’nogov, Vladislav Nikolaevich
7 Kraaijevanger, J. F. B. M.
7 Liu, Changying
...and 2,985 more Authors
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Cited in 346 Serials

269 Applied Numerical Mathematics
229 Journal of Computational and Applied Mathematics
160 Journal of Computational Physics
134 Applied Mathematics and Computation
131 BIT
102 Numerical Algorithms
80 Computers & Mathematics with Applications
72 Journal of Scientific Computing
56 International Journal of Computer Mathematics
54 Mathematics of Computation
51 Numerische Mathematik
44 Computer Methods in Applied Mechanics and Engineering
39 Computing
36 SIAM Journal on Scientific Computing
34 BIT. Nordisk Tidskrift for Informationsbehandling
29 Computer Physics Communications
29 Mathematical Methods in the Applied Sciences
29 Mathematics and Computers in Simulation
29 Computational and Applied Mathematics
29 Journal of Mathematical Chemistry
28 Computers and Fluids
26 SIAM Journal on Numerical Analysis
20 Calcolo
20 Advances in Computational Mathematics
18 Applied Mathematical Modelling
17 Applied Mathematics Letters
17 Communications in Nonlinear Science and Numerical Simulation
16 Journal of Applied Mathematics and Computing
14 Mathematical Problems in Engineering
14 Foundations of Computational Mathematics
13 Japan Journal of Industrial and Applied Mathematics
12 Numerical Methods for Partial Differential Equations
10 Journal of the Nigerian Mathematical Society
9 Chaos, Solitons and Fractals
9 International Journal for Numerical Methods in Engineering
9 Mathematical and Computer Modelling
9 Advances in Difference Equations
9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 Physica D
8 Numerical Linear Algebra with Applications
8 Discrete Dynamics in Nature and Society
8 Journal of Applied Mathematics
7 Computational Mathematics and Mathematical Physics
7 Linear Algebra and its Applications
7 Chaos
7 Mathematical Modelling and Analysis
7 Communications in Computational Physics
7 International Journal of Applied and Computational Mathematics
7 Communications on Applied Mathematics and Computation
6 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
6 Bulletin of the Iranian Mathematical Society
6 Celestial Mechanics and Dynamical Astronomy
6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
6 Discrete and Continuous Dynamical Systems
6 Abstract and Applied Analysis
6 International Journal of Computational Methods
6 Mediterranean Journal of Mathematics
6 Journal of Theoretical Biology
5 Acta Mechanica
5 Journal of Fluid Mechanics
5 Journal of the Franklin Institute
5 Automatica
5 Publications of the Research Institute for Mathematical Sciences, Kyoto University
5 Journal of Difference Equations and Applications
5 Discrete and Continuous Dynamical Systems. Series B
5 Discrete and Continuous Dynamical Systems. Series S
5 Advances in Applied Mathematics and Mechanics
5 Afrika Matematika
5 Axioms
4 Communications in Mathematical Physics
4 International Journal for Numerical Methods in Fluids
4 Journal of Mathematical Analysis and Applications
4 Physics Letters. A
4 Advances in Mathematics
4 Journal of Optimization Theory and Applications
4 Numerical Functional Analysis and Optimization
4 Computational Mechanics
4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
4 Nonlinear Dynamics
4 International Journal of Nonlinear Sciences and Numerical Simulation
4 International Journal of Modern Physics C
4 The ANZIAM Journal
4 Computational Methods in Applied Mathematics
4 Oberwolfach Reports
4 Symmetry
4 International Journal of Structural Stability and Dynamics
4 Statistics and Computing
4 Journal of the Korean Society for Industrial and Applied Mathematics
4 Journal of Computational Dynamics
4 Journal of Mathematical Modeling
3 Journal of Mathematical Physics
3 Physica A
3 Physics Reports
3 Ukrainian Mathematical Journal
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 Acta Applicandae Mathematicae
3 Journal of Computational Mathematics
...and 246 more Serials
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Cited in 55 Fields

2,199 Numerical analysis (65-XX)
917 Ordinary differential equations (34-XX)
335 Partial differential equations (35-XX)
215 Fluid mechanics (76-XX)
135 Probability theory and stochastic processes (60-XX)
133 Dynamical systems and ergodic theory (37-XX)
105 Biology and other natural sciences (92-XX)
71 Mechanics of particles and systems (70-XX)
64 Systems theory; control (93-XX)
60 Mechanics of deformable solids (74-XX)
59 Integral equations (45-XX)
59 Computer science (68-XX)
50 Approximations and expansions (41-XX)
48 Quantum theory (81-XX)
42 Combinatorics (05-XX)
39 Associative rings and algebras (16-XX)
38 Operations research, mathematical programming (90-XX)
37 Calculus of variations and optimal control; optimization (49-XX)
29 Statistics (62-XX)
25 Statistical mechanics, structure of matter (82-XX)
21 Linear and multilinear algebra; matrix theory (15-XX)
21 Optics, electromagnetic theory (78-XX)
21 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
18 Nonassociative rings and algebras (17-XX)
18 Classical thermodynamics, heat transfer (80-XX)
17 Operator theory (47-XX)
15 Geophysics (86-XX)
15 Information and communication theory, circuits (94-XX)
12 Real functions (26-XX)
12 Global analysis, analysis on manifolds (58-XX)
11 History and biography (01-XX)
10 Difference and functional equations (39-XX)
8 Relativity and gravitational theory (83-XX)
7 General and overarching topics; collections (00-XX)
7 Special functions (33-XX)
7 Differential geometry (53-XX)
6 Category theory; homological algebra (18-XX)
6 Topological groups, Lie groups (22-XX)
6 Integral transforms, operational calculus (44-XX)
5 Number theory (11-XX)
5 Astronomy and astrophysics (85-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
4 Functional analysis (46-XX)
3 Commutative algebra (13-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Algebraic geometry (14-XX)
2 Functions of a complex variable (30-XX)
1 Mathematical logic and foundations (03-XX)
1 Field theory and polynomials (12-XX)
1 Measure and integration (28-XX)
1 Several complex variables and analytic spaces (32-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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