John C. Butcher - Author Profile

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Butcher, John C.

Author ID:	butcher.john-c
Published as:	Butcher, J. C.; Butcher, John C.; Butcher, John more...less
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:	161 Publications since 1956, including 5 Books and 1 Additional arXiv Preprint
	6 Contributions as Editor · 2 Further Contributions
Reviewing Activity:	43 Reviews
Biographic References:	2 Publications
Co-Authors:	49 Co-Authors with 69 Joint Publications
	973 Co-Co-Authors

all top 5

Co-Authors

96	single-authored
14	Jackiewicz, Zdzislaw
5	Cash, Jeff R.
5	Chartier, Philippe
4	Chan, T. M. H.
4	Podhaisky, Helmut
3	Burrage, Kevin
3	Chen, D. J. L.
3	Hill, Adrian T.
3	Imran, Gulshad
3	Miyatake, Yuto
2	Abdi, Ali
2	Chan, Robert Peng Kong
2	Chipman, F. H.
2	Diamantakis, M. T.
2	Norton, Terence J. T.
2	Sato, Shun
2	van der Houwen, Pieter J.
2	Wanner, Gerhard
1	Ahmad, Saghir
1	Baker, Christopher Thomas Hale
1	Brezinski, Claude
1	Cooper, Gavin J.
1	Corless, Robert Malcolm
1	D’Ambrosio, Raffaele
1	Delves, L. M.
1	Elhay, Sylvan
1	Enright, Wayne H.
1	Gander, Martin Jakob
1	Gautschi, Walter
1	Gladwell, Ian
1	Gonzalez-Vega, Laureano
1	Habib, Yousaf
1	Heard, A. D.
1	Henell, M. A.
1	Hewitt, L. L.
1	Hojjati, Gholamreza
1	Johnston, P. B.
1	Kautsky, Jaroslav
1	Lambert, J. D.
1	Lorentzen, Lisa
1	Mazzia, Francesca
1	Messel, Harry
1	Milovanović, Gradimir V.
1	Mitsui, Taketomo
1	Mittelmann, Hans Detlef
1	Moir, Nicolette
1	Moore, Gerald
1	O’Sullivan, A. E.
1	Prothero, A.
1	Rabinowitz, Philip
1	Rattenbury, Nicolette
1	Robertson, H. N.
1	Russell, Robert D.
1	Sameh, Ahmed H.
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	Wait, R.
1	Watt, J. M.
1	Weiner, Rüdiger

all top 5

Serials

28	Applied Numerical Mathematics
24	Numerical Algorithms
22	BIT
10	Mathematics of Computation
7	SIAM Journal on Numerical Analysis
6	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	Springer Series in Computational Mathematics
1	Axioms
1	Contemporary Mathematicians

all top 5

Fields

150	Numerical analysis (65-XX)
104	Ordinary differential equations (34-XX)
8	Dynamical systems and ergodic theory (37-XX)
7	General and overarching topics; collections (00-XX)
7	History and biography (01-XX)
4	Combinatorics (05-XX)
3	Number theory (11-XX)
3	Approximations and expansions (41-XX)
2	Mechanics of particles and systems (70-XX)
1	Linear and multilinear algebra; matrix theory (15-XX)
1	Real functions (26-XX)
1	Partial differential equations (35-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)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

147 Publications have been cited 4,551 times in 2,650 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.	432	2008
Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004 Butcher, J. C.	285	2016
Implicit Runge-Kutta processes. Zbl 0123.11701 Butcher, J. C.	262	1964
Numerical methods for ordinary differential equations. Zbl 1040.65057 Butcher, J. C.	194	2003
Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043 Burrage, Kevin; Butcher, J. C.	144	1979
An algebraic theory of integration methods. Zbl 0258.65070 Butcher, J. C.	144	1972
Coefficients for the study of Runge-Kutta integration processes. Zbl 0223.65031 Butcher, J. C.	134	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.	72	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.	65	2006
Second derivative methods with RK stability. Zbl 1084.65069 Butcher, J. C.; Hojjati, G.	59	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.	50	1964
Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043 Butcher, J. C.; Jackiewicz, Z.	49	1993
A modified multistep method for the numerical integration of ordinary differential equations. Zbl 0125.07102 Butcher, J. C.	49	1965
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.	37	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
Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063 Butcher, J. C.	29	2000
A history of Runge-Kutta methods. Zbl 0858.65073 Butcher, J. C.	29	1996
Trees and numerical methods for ordinary differential equations. Zbl 1184.65072 Butcher, J. C.	29	2010
On the attainable order of Runge-Kutta methods. Zbl 0132.36401 Butcher, J. C.	28	1965
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
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 approach to error estimation for general linear methods. Zbl 1032.65088 Butcher, J. C.; Jackiewicz, Z.	16	2003
A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058 Butcher, J. C.; Chen, D. J. L.	16	2000
B-series. Algebraic analysis of numerical methods. Zbl 07332820 Butcher, John C.	16	2021
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
ARK methods for stiff problems. Zbl 1070.65059 Butcher, John C.; Rattenbury, Nicolette	15	2005
Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078 Butcher, J. C.; Jackiewicz, Z.	15	2004
Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072 Butcher, J. C.; Cash, J. R.	14	1990
The existence of symplectic general linear methods. Zbl 1176.65080 Butcher, J. C.; Hewitt, L. L.	13	2009
Runge-Kutta methods: Some historical notes. Zbl 0867.65038 Butcher, J. C.; Wanner, G.	13	1996
Stability of numerical methods for ordinary differential equations. Zbl 1016.65059 Butcher, J. C.; Heard, A. D.	13	2002
DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064 Butcher, J. C.; Diamantakis, M. T.	13	1998
The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089 Butcher, J. C.; Chartier, P.	13	1999
Trees, B-series and exponential integrators. Zbl 1185.65121 Butcher, J. C.	13	2010
On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080 Butcher, J. C.; Podhaisky, H.	12	2006
The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039 Butcher, J. C.; Sanz-Serna, J. M.	12	1996
DESI methods for stiff initial-value problems. Zbl 0884.65077 Butcher, J. C.; Cash, J. R.; Diamantakis, M. T.	12	1996
On A-stable implicit Runge-Kutta methods. Zbl 0378.65039 Butcher, J. C.	12	1977
Order and stability of generalized Padé approximations. Zbl 1182.65111 Butcher, J. C.	11	2009
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
A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081 Butcher, J. C.; Jackiewicz, Z.	11	2001
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
The non-existence of ten stage eighth order explicit Runge-Kutta methods. Zbl 0579.65066 Butcher, J. C.	11	1985
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
The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040 Butcher, J. C.	10	1992
Towards efficient implementation of singly-implicit methods. Zbl 0639.65041 Butcher, J. C.	10	1988
A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076 Butcher, J. C.; Chartier, P.	10	1997
A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048 Butcher, J. C.; Wright, W. M.	10	2003
Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068 Butcher, J. C.	9	2013
The adaptation of STRIDE to delay differential equations. Zbl 0776.65049 Butcher, J. C.	9	1992
General linear method: A survey. Zbl 0619.65057 Butcher, J. C.	9	1985
Applications of doubly companion matrices. Zbl 1089.65065 Butcher, J. C.; Wright, W. M.	9	2006
Thirty years of G-stability. Zbl 1105.65085 Butcher, J. C.	9	2006
General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059 Butcher, J. C.	9	1993
On the integration processes of A. Huta. Zbl 0223.65032 Butcher, J. C.	9	1963
Symmetric general linear methods. Zbl 1355.65095 Butcher, J. C.; Hill, A. T.; Norton, T. J. T.	8	2016
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
Some implementation schemes for implicit Runge-Kutta methods. Zbl 0447.65042 Butcher, J. C.	8	1980
On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119 Butcher, J. C.	7	2009
Generalized Padé approximations to the exponential function. Zbl 0789.65063 Butcher, J. C.; Chipman, F. H.	7	1992
A transformation for the analysis of DIMSIMs. Zbl 0814.65079 Butcher, J. C.	7	1994
Order and stability of parallel methods for stiff problems. Zbl 0884.65090 Butcher, J. C.	7	1997
Error estimation for Nordsieck methods. Zbl 1012.65083 Butcher, J. C.; Jackiewicz, Z.	7	2002
Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002 Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar	7	2011
On sequences of imbedded integration rules. Zbl 0635.41024 Rabinowitz, Philip; Kautsky, Jaroslav; Elhay, Sylvan; Butcher, John C.	6	1987
Random sampling from the normal distribution. Zbl 0094.13503 Butcher, J. C.	6	1961
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
An order bound for Runge-Kutta methods. Zbl 0318.65030 Butcher, J. C.	5	1975
Applications of order arrows. Zbl 1241.65070 Abdi, A.; Butcher, J. C.	5	2012
Optimal order and stepsize sequences. Zbl 0615.65076 Butcher, J. C.	5	1986
Parallel general linear methods for stiff ordinary differential and differential algebraic equations. Zbl 0833.65073 Butcher, J. C.; Chartier, P.	5	1995
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.	16	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.	285	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.	13	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
B-series and B-series coefficients. Zbl 1182.65112 Butcher, J. C.	1	2009
Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041 Butcher, J. C.	432	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.	65	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.	9	2006
Thirty years of G-stability. Zbl 1105.65085 Butcher, J. C.	9	2006
Second derivative methods with RK stability. Zbl 1084.65069 Butcher, J. C.; Hojjati, G.	59	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.	194	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.	13	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.	29	1996
Runge-Kutta methods: Some historical notes. Zbl 0867.65038 Butcher, J. C.; Wanner, G.	13	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.	12	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
Parallel general linear methods for stiff ordinary differential and differential algebraic equations. Zbl 0833.65073 Butcher, J. C.; Chartier, P.	5	1995
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
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
Some orbital test problems. Zbl 0806.65068 Butcher, J. C.	2	1994
Initial value problems: Numerical methods and mathematics. Zbl 0817.65059 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
...and 47 more Documents

all cited Publications top 5 cited Publications

all top 5

Cited by 3,115 Authors

78	Butcher, John C.
76	Jackiewicz, Zdzislaw
50	Tsitouras, Charalampos
49	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.
24	Ramos, Higinio
22	Izzo, Giuseppe
21	Burrage, Kevin
21	Podhaisky, Helmut
21	You, Xiong
20	Hairer, Ernst
20	Sanz-Serna, Jesús María
19	Cash, Jeff R.
19	Montijano, Juan Ignacio
19	Spijker, Marc N.
18	González-Pinto, Severiano
17	Ketcheson, David I.
17	Li, Shoufu
17	van der Houwen, Pieter J.
16	Famelis, Ioannis Th.
16	Sandu, Adrian
16	Wu, Xinyuan
15	Brugnano, Luigi
15	Rández, Luis
15	Schmitt, Bernhard A.
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	Liu, Mingzhu
13	Sommeijer, Ben P.
13	Zennaro, Marino
12	Blanes, Sergio
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	Evans, David John
10	Gottlieb, Sigal
10	Huang, Chengming
10	Iavernaro, Felice
10	Ranocha, Hendrik
10	Verner, James H.
9	Cardone, Angelamaria
9	Casas, Fernando
9	Corless, Robert Malcolm
9	Debrabant, Kristian
9	Ebrahimi-Fard, Kurusch
9	Faragó, István
9	Hill, Adrian T.
9	Kvaerno, Anne
9	Lubich, Christian
9	McLachlan, Robert I.
9	Nørsett, Syvert Paul
9	Rufai, Mufutau Ajani
9	Scherer, Rudolf
9	Tian, Hongjiong
9	Vanden Berghe, Guido
9	Vermiglio, Rossana
9	Zhao, Weidong
8	Bruned, Yvain
8	Havasi, Ágnes
8	Hernandez-Abreu, Domingo
8	Ibrahim, Zarina Bibi Binti
8	Magherini, Cecilia
8	Martín-Vaquero, Jesús
8	Mitsui, Taketomo
8	Miyatake, Yuto
8	Murua, Ander
8	Schneid, Josef
8	Wang, Bin
8	Wang, Zhongqing
8	Wen, Liping
8	Yang, Zhanwen
8	Yu, Yuexin
7	Axelsson, Axel Owe Holger
7	Bellen, Alfredo
7	De Meyer, Hans E.
7	Dormand, John R.
7	Fazio, Riccardo
7	Georgiev, Krassimir
...and 3,015 more Authors

all top 5

Cited in 351 Serials

275	Applied Numerical Mathematics
230	Journal of Computational and Applied Mathematics
161	Journal of Computational Physics
134	Applied Mathematics and Computation
131	BIT
104	Numerical Algorithms
80	Computers & Mathematics with Applications
73	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
18	Communications in Nonlinear Science and Numerical Simulation
17	Applied Mathematics Letters
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	International Journal for Numerical Methods in Engineering
12	Numerical Methods for Partial Differential Equations
10	Journal of the Nigerian Mathematical Society
9	Chaos, Solitons and Fractals
9	Mathematical and Computer Modelling
9	Journal of Applied Mathematics
9	Advances in Difference Equations
9	European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
9	Communications in Computational Physics
8	Physica D
8	Numerical Linear Algebra with Applications
8	Discrete Dynamics in Nature and Society
8	Communications on Applied Mathematics and Computation
7	Computational Mathematics and Mathematical Physics
7	Linear Algebra and its Applications
7	Chaos
7	Mathematical Modelling and Analysis
7	International Journal of Applied and Computational Mathematics
6	Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
6	Journal of Optimization Theory and Applications
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	Abstract and Applied Analysis
6	International Journal of Computational Methods
6	Mediterranean Journal of Mathematics
6	Journal of Theoretical Biology
6	Journal of Computational Dynamics
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
5	Discrete and Continuous Dynamical Systems. Series B
5	Oberwolfach Reports
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	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	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 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 251 more Serials

all top 5

Cited in 55 Fields

2,229	Numerical analysis (65-XX)
915	Ordinary differential equations (34-XX)
341	Partial differential equations (35-XX)
217	Fluid mechanics (76-XX)
138	Probability theory and stochastic processes (60-XX)
136	Dynamical systems and ergodic theory (37-XX)
105	Biology and other natural sciences (92-XX)
71	Mechanics of particles and systems (70-XX)
66	Systems theory; control (93-XX)
61	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)
44	Combinatorics (05-XX)
42	Calculus of variations and optimal control; optimization (49-XX)
40	Associative rings and algebras (16-XX)
37	Operations research, mathematical programming (90-XX)
31	Statistics (62-XX)
25	Statistical mechanics, structure of matter (82-XX)
22	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)
19	Classical thermodynamics, heat transfer (80-XX)
18	Nonassociative rings and algebras (17-XX)
18	Operator theory (47-XX)
16	Geophysics (86-XX)
16	Information and communication theory, circuits (94-XX)
13	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	General and overarching topics; collections (00-XX)
8	Relativity and gravitational theory (83-XX)
7	Category theory; homological algebra (18-XX)
7	Special functions (33-XX)
7	Differential geometry (53-XX)
6	Topological groups, Lie groups (22-XX)
6	Integral transforms, operational calculus (44-XX)
5	Number theory (11-XX)
5	Harmonic analysis on Euclidean spaces (42-XX)
5	Astronomy and astrophysics (85-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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