Edit Profile Butcher, John C. Compute Distance To: Compute 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 all top 5 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. all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0616.65072Butcher, J. C. 562 1987 Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041Butcher, J. C. 320 2008 Implicit Runge-Kutta processes. Zbl 0123.11701Butcher, J. C. 202 1964 Numerical methods for ordinary differential equations. Zbl 1040.65057Butcher, J. C. 201 2003 Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043Burrage, Kevin; Butcher, J. C. 121 1979 Coefficients for the study of Runge-Kutta integration processes. Zbl 0223.65031Butcher, J. C. 114 1963 Non-linear stability of a general class of differential equation methods. Zbl 0431.65051Burrage, Kevin; Butcher, J. C. 109 1980 An algebraic theory of integration methods. Zbl 0258.65070Butcher, J. C. 100 1972 On the implementation of implicit Runge-Kutta methods. Zbl 0336.65037Butcher, J. C. 87 1976 Some numerical methods for stiff problems. Zbl 1032.65512Butcher, J. C. 78 2003 On Runge-Kutta processes of high order. Zbl 0244.65046Butcher, J. C. 70 1964 Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004Butcher, J. C. 66 2016 Diagonally-implicit multi-stage integration methods. Zbl 0773.65046Butcher, J. C. 63 1993 On the convergence of numerical solutions to ordinary differential equations. Zbl 0141.13504Butcher, J. C. 63 1966 A stability property of implicit Runge-Kutta methods. Zbl 0333.65031Butcher, J. C. 62 1975 An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040Burrage, K.; Butcher, J. C.; Chipman, F. H. 60 1980 The order of numerical methods for ordinary differential equations. Zbl 0278.65073Butcher, J. C. 58 1973 General linear methods. Zbl 1113.65072Butcher, J. C. 51 2006 Integration processes based on Radau quadrature formulas. Zbl 0123.11702Butcher, J. C. 42 1964 Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043Butcher, J. C.; Jackiewicz, Z. 39 1993 A modified multistep method for the numerical integration of ordinary differential equations. Zbl 0125.07102Butcher, J. C. 37 1965 Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044Butcher, J. C.; Jackiewicz, Z. 35 1997 Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations. Zbl 0865.65056Butcher, J. C.; Jackiewicz, Z. 34 1996 The construction of practical general linear methods. Zbl 1046.65054Butcher, J. C.; Wright, W. M. 33 2003 Second derivative methods with RK stability. Zbl 1084.65069Butcher, J. C.; Hojjati, G. 32 2005 Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080Butcher, J. C.; Jackiewicz, Z. 31 1998 An iteration scheme for implicit Runge-Kutta methods. Zbl 0525.65052Cooper, G. J.; Butcher, J. C. 31 1983 A transformed implicit Runge-Kutta method. Zbl 0439.65057Butcher, J. C. 29 1979 On the attainable order of Runge-Kutta methods. Zbl 0132.36401Butcher, J. C. 26 1965 The effective order of Runge-Kutta methods. Zbl 0185.41301Butcher, J. C. 25 1969 Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077Butcher, J. C.; Tracogna, S. 21 1997 Trees and numerical methods for ordinary differential equations. Zbl 1184.65072Butcher, J. C. 20 2010 Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063Butcher, J. C. 19 2000 General linear methods for stiff differential equations. Zbl 0983.65085Butcher, J. C. 18 2001 A history of Runge-Kutta methods. Zbl 0858.65073Butcher, J. C. 18 1996 The control of parasitism in \(G\)-symplectic methods. Zbl 1309.65148Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T. 17 2014 Nordsieck representation of DIMSIMs. Zbl 0920.65043Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 16 1997 Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068Butcher, J. C.; Jackiewicz, Z.; Wright, W. M. 15 2007 Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083Butcher, J. C.; Jackiewicz, Z. 15 2004 A new approach to error estimation for general linear methods. Zbl 1032.65088Butcher, J. C.; Jackiewicz, Z. 15 2003 Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 15 1999 ARK methods for stiff problems. Zbl 1070.65059Butcher, John C.; Rattenbury, Nicolette 14 2005 Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072Butcher, J. C.; Cash, J. R. 14 1990 The equivalence of algebraic stability and AN-stability. Zbl 0637.65083Butcher, J. C. 14 1987 Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078Butcher, J. C.; Jackiewicz, Z. 13 2004 A multistep generalization of Runge-Kutta methods with four or five stages. Zbl 0168.13901Butcher, J. C. 13 1967 The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089Butcher, J. C.; Chartier, P. 12 1999 A nonlinear optimization approach to the construction of general linear methods of high order. Zbl 0879.65051Butcher, J. C.; Jackiewicz, Z.; Mittelmann, H. D. 12 1997 On A-stable implicit Runge-Kutta methods. Zbl 0378.65039Butcher, J. C. 12 1977 A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232Miyatake, Yuto; Butcher, John C. 11 2016 A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058Butcher, J. C.; Chen, D. J. L. 11 2000 DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064Butcher, J. C.; Diamantakis, M. T. 11 1998 DESI methods for stiff initial-value problems. Zbl 0884.65077Butcher, J. C.; Cash, J. R.; Diamantakis, M. T. 11 1996 On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080Butcher, J. C.; Podhaisky, H. 10 2006 A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081Butcher, J. C.; Jackiewicz, Z. 10 2001 A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076Butcher, J. C.; Chartier, P. 10 1997 An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085Butcher, J. C. 10 1997 Runge-Kutta methods: Some historical notes. Zbl 0867.65038Butcher, J. C.; Wanner, G. 10 1996 The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040Butcher, J. C. 10 1992 Towards efficient implementation of singly-implicit methods. Zbl 0639.65041Butcher, J. C. 10 1988 Linear and non-linear stability for general linear methods. Zbl 0623.65074Butcher, J. C. 10 1987 A generalization of singly-implicit methods. Zbl 0484.65048Butcher, J. C. 10 1981 Trees, B-series and exponential integrators. Zbl 1185.65121Butcher, J. C. 9 2010 The existence of symplectic general linear methods. Zbl 1176.65080Butcher, J. C.; Hewitt, L. L. 9 2009 Order and stability of generalized Padé approximations. Zbl 1182.65111Butcher, J. C. 9 2009 A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048Butcher, J. C.; Wright, W. M. 9 2003 The non-existence of ten stage eighth order explicit Runge-Kutta methods. Zbl 0579.65066Butcher, J. C. 9 1985 Order bounds for second derivative approximations. Zbl 1247.65103Abdi, A.; Butcher, J. C. 8 2012 High order A-stable numerical methods for stiff problems. Zbl 1203.65106Butcher, J. C. 8 2005 Stability of numerical methods for ordinary differential equations. Zbl 1016.65059Butcher, J. C.; Heard, A. D. 8 2002 The \(A\)-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057Butcher, J. C. 8 2002 General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059Butcher, J. C. 8 1993 The adaptation of STRIDE to delay differential equations. Zbl 0776.65049Butcher, J. C. 8 1992 General linear method: A survey. Zbl 0619.65057Butcher, J. C. 8 1985 Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272Butcher, John C.; D’Ambrosio, Raffaele 7 2017 Thirty years of G-stability. Zbl 1105.65085Butcher, J. C. 7 2006 Linear multistep methods as irreducible general linear methods. Zbl 1102.65078Butcher, J. C.; Hill, A. T. 7 2006 Applications of doubly companion matrices. Zbl 1089.65065Butcher, J. C.; Wright, W. M. 7 2006 Error estimation for Nordsieck methods. Zbl 1012.65083Butcher, J. C.; Jackiewicz, Z. 7 2002 General linear methods. Zbl 0874.65057Butcher, J. C. 7 1996 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039Butcher, J. C.; Sanz-Serna, J. M. 7 1996 A transformation for the analysis of DIMSIMs. Zbl 0814.65079Butcher, J. C. 7 1994 Some implementation schemes for implicit Runge-Kutta methods. Zbl 0447.65042Butcher, J. C. 7 1980 On the integration processes of A. Huta. Zbl 0223.65032Butcher, J. C. 7 1963 Symmetric general linear methods. Zbl 1355.65095Butcher, J. C.; Hill, A. T.; Norton, T. J. T. 6 2016 Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068Butcher, J. C. 6 2013 On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119Butcher, J. C. 6 2009 Generalized Padé approximations to the exponential function. Zbl 0789.65063Butcher, J. C.; Chipman, F. H. 6 1992 On sequences of imbedded integration rules. Zbl 0635.41024Rabinowitz, Philip; Kautsky, Jaroslav; Elhay, Sylvan; Butcher, John C. 6 1987 An application of the Runge-Kutta space. Zbl 0555.65045Butcher, J. C. 6 1984 Random sampling from the normal distribution. Zbl 0094.13503Butcher, J. C. 6 1961 Applications of order arrows. Zbl 1241.65070Abdi, A.; Butcher, J. C. 5 2012 Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar 5 2011 Forty-five years of A-stability. Zbl 1191.65109Butcher, J. C. 5 2009 Order and effective order. Zbl 0927.65095Butcher, J. C. 5 1998 Efficient Runge-Kutta integrators for index-2 differential algebraic equations. Zbl 0899.65048Butcher, J. C.; Chan, R. P. K. 5 1998 Defect correction for two-point boundary value problems on nonequidistant meshes. Zbl 0828.65102Butcher, J. C.; Cash, J. R.; Moore, G.; Russell, R. D. 5 1995 Optimal order and stepsize sequences. Zbl 0615.65076Butcher, J. C. 5 1986 An order bound for Runge-Kutta methods. Zbl 0318.65030Butcher, J. C. 5 1975 Symplectic effective order methods. Zbl 1291.65359Butcher, John C.; Imran, Gulshad 4 2014 Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272Butcher, John C.; D’Ambrosio, Raffaele 7 2017 A G-symplectic method with order 6. Zbl 1367.65190Butcher, John C.; Imran, Gulshad; Podhaisky, Helmut 3 2017 Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004Butcher, J. C. 66 2016 A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232Miyatake, Yuto; Butcher, John C. 11 2016 Symmetric general linear methods. Zbl 1355.65095Butcher, J. C.; Hill, A. T.; Norton, T. J. T. 6 2016 Order conditions for G-symplectic methods. Zbl 1338.65185Butcher, John C.; Imran, Gulshad 3 2015 The cohesiveness of G-symplectic methods. Zbl 1330.65192Butcher, J. C. 3 2015 Runge-Kutta methods for ordinary differential equations. Zbl 1330.65109Butcher, J. C. 1 2015 The control of parasitism in \(G\)-symplectic methods. Zbl 1309.65148Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T. 17 2014 Symplectic effective order methods. Zbl 1291.65359Butcher, John C.; Imran, Gulshad 4 2014 Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068Butcher, J. C. 6 2013 Predictor-corrector Obreshkov pairs. Zbl 1307.65099Butcher, John C.; Sehnalová, Pavla 3 2013 Order bounds for second derivative approximations. Zbl 1247.65103Abdi, A.; Butcher, J. C. 8 2012 Applications of order arrows. Zbl 1241.65070Abdi, A.; Butcher, J. C. 5 2012 Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar 5 2011 Trees and numerical methods for ordinary differential equations. Zbl 1184.65072Butcher, J. C. 20 2010 Trees, B-series and exponential integrators. Zbl 1185.65121Butcher, J. C. 9 2010 The tree and forest spaces with applications to initial-value problem methods. Zbl 1205.65211Butcher, J. C.; Chan, T. M. H. 3 2010 B-series and B-series coefficients. Zbl 1432.65096Butcher, J. C. 1 2010 The existence of symplectic general linear methods. Zbl 1176.65080Butcher, J. C.; Hewitt, L. L. 9 2009 Order and stability of generalized Padé approximations. Zbl 1182.65111Butcher, J. C. 9 2009 On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119Butcher, J. C. 6 2009 Forty-five years of A-stability. Zbl 1191.65109Butcher, J. C. 5 2009 General linear methods for ordinary differential equations. Zbl 1159.65333Butcher, John 3 2009 Practical Runge-Kutta methods for scientific computation. Zbl 1178.65083Butcher, J. C. 2 2009 Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041Butcher, J. C. 320 2008 Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068Butcher, J. C.; Jackiewicz, Z.; Wright, W. M. 15 2007 General linear methods. Zbl 1113.65072Butcher, J. C. 51 2006 On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080Butcher, J. C.; Podhaisky, H. 10 2006 Thirty years of G-stability. Zbl 1105.65085Butcher, J. C. 7 2006 Linear multistep methods as irreducible general linear methods. Zbl 1102.65078Butcher, J. C.; Hill, A. T. 7 2006 Applications of doubly companion matrices. Zbl 1089.65065Butcher, J. C.; Wright, W. M. 7 2006 Second derivative methods with RK stability. Zbl 1084.65069Butcher, J. C.; Hojjati, G. 32 2005 ARK methods for stiff problems. Zbl 1070.65059Butcher, John C.; Rattenbury, Nicolette 14 2005 High order A-stable numerical methods for stiff problems. Zbl 1203.65106Butcher, J. C. 8 2005 Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083Butcher, J. C.; Jackiewicz, Z. 15 2004 Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078Butcher, J. C.; Jackiewicz, Z. 13 2004 Numerical methods for ordinary differential equations. Zbl 1040.65057Butcher, J. C. 201 2003 Some numerical methods for stiff problems. Zbl 1032.65512Butcher, J. C. 78 2003 The construction of practical general linear methods. Zbl 1046.65054Butcher, J. C.; Wright, W. M. 33 2003 A new approach to error estimation for general linear methods. Zbl 1032.65088Butcher, J. C.; Jackiewicz, Z. 15 2003 A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048Butcher, J. C.; Wright, W. M. 9 2003 Experiments with a new fifth order method. Zbl 1030.65081Butcher, John C.; Moir, Nicolette 2 2003 Stability of numerical methods for ordinary differential equations. Zbl 1016.65059Butcher, J. C.; Heard, A. D. 8 2002 The \(A\)-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057Butcher, J. C. 8 2002 Error estimation for Nordsieck methods. Zbl 1012.65083Butcher, J. C.; Jackiewicz, Z. 7 2002 A new approach to the algebraic structures for integration methods. Zbl 1016.65047Butcher, J. C.; Chan, T. M. H. 2 2002 Nordsieck methods with an off-step point. Zbl 1012.65074Butcher, 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 1017.00022Butcher, J. C. (ed.); Enright, W. H. (ed.); Mazzia, F. (ed.); Söderling, G. (ed.); van der Houwen, P. J. (ed.) 1 2002 General linear methods for stiff differential equations. Zbl 0983.65085Butcher, J. C. 18 2001 A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081Butcher, J. C.; Jackiewicz, Z. 10 2001 On the implementation of ESIRK methods for stiff IVPs. Zbl 0974.65075Butcher, J. C.; Chen, D. J. L. 3 2001 Variable stepsize schemes for effective order methods and enhanced order composition methods. Zbl 0976.65067Butcher, J. C.; Chan, T. M. H. 2 2001 Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063Butcher, J. C. 19 2000 A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058Butcher, J. C.; Chen, D. J. L. 11 2000 Multi-step zero approximations for stepsize control. Zbl 0951.65072Butcher, J. C.; Chan, T. M. H. 2 2000 The choice of parameters in parallel general linear methods for stiff problems. Zbl 0949.65076Butcher, J. C.; Singh, A. D. 2 2000 Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 15 1999 The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089Butcher, J. C.; Chartier, P. 12 1999 Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080Butcher, J. C.; Jackiewicz, Z. 31 1998 DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064Butcher, J. C.; Diamantakis, M. T. 11 1998 Order and effective order. Zbl 0927.65095Butcher, J. C. 5 1998 Efficient Runge-Kutta integrators for index-2 differential algebraic equations. Zbl 0899.65048Butcher, J. C.; Chan, R. P. K. 5 1998 ESIRK methods and variable stepsize. Zbl 0927.65096Butcher, J. C.; Chen, D. J. L. 3 1998 ARK methods up to order five. Zbl 0907.65069Butcher, J. C. 2 1998 Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044Butcher, J. C.; Jackiewicz, Z. 35 1997 Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077Butcher, J. C.; Tracogna, S. 21 1997 Nordsieck representation of DIMSIMs. Zbl 0920.65043Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 16 1997 A nonlinear optimization approach to the construction of general linear methods of high order. Zbl 0879.65051Butcher, J. C.; Jackiewicz, Z.; Mittelmann, H. D. 12 1997 A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076Butcher, J. C.; Chartier, P. 10 1997 An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085Butcher, J. C. 10 1997 Order and stability of parallel methods for stiff problems. Zbl 0884.65090Butcher, J. C. 3 1997 Numerical methods for differential equations and applications. Zbl 0912.65064Butcher, J. C. 1 1997 Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations. Zbl 0865.65056Butcher, J. C.; Jackiewicz, Z. 34 1996 A history of Runge-Kutta methods. Zbl 0858.65073Butcher, J. C. 18 1996 DESI methods for stiff initial-value problems. Zbl 0884.65077Butcher, J. C.; Cash, J. R.; Diamantakis, M. T. 11 1996 Runge-Kutta methods: Some historical notes. Zbl 0867.65038Butcher, J. C.; Wanner, G. 10 1996 General linear methods. Zbl 0874.65057Butcher, J. C. 7 1996 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039Butcher, J. C.; Sanz-Serna, J. M. 7 1996 Defect correction for two-point boundary value problems on nonequidistant meshes. Zbl 0828.65102Butcher, 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 0833.65073Butcher, J. C.; Chartier, P. 4 1995 On fifth order Runge-Kutta methods. Zbl 0837.65073Butcher, J. C. 3 1995 An introduction to DIMSIMs. Zbl 0838.65078Butcher, J. C. 1 1995 A transformation for the analysis of DIMSIMs. Zbl 0814.65079Butcher, J. C. 7 1994 Initial value problems: Numerical methods and mathematics. Zbl 0817.65059Butcher, J. C. 2 1994 Some orbital test problems. Zbl 0806.65068Butcher, J. C. 1 1994 Diagonally-implicit multi-stage integration methods. Zbl 0773.65046Butcher, J. C. 63 1993 Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043Butcher, J. C.; Jackiewicz, Z. 39 1993 General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059Butcher, J. C. 8 1993 The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040Butcher, J. C. 10 1992 The adaptation of STRIDE to delay differential equations. Zbl 0776.65049Butcher, J. C. 8 1992 Generalized Padé approximations to the exponential function. Zbl 0789.65063Butcher, J. C.; Chipman, F. H. 6 1992 On symmetrizers for Gauss method. Zbl 0723.65045Butcher, J. C.; Chan, R. P. K. 2 1992 Some new hybrid methods for initial value problems. Zbl 0769.65037Butcher, J. C. 2 1992 Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072Butcher, J. C.; Cash, J. R. 14 1990 Order, stepsize and stiffness switching. Zbl 0719.65059Butcher, J. C. 4 1990 Towards efficient implementation of singly-implicit methods. Zbl 0639.65041Butcher, J. C. 10 1988 On a class of matrices with real eigenvalues. Zbl 0667.15006Butcher, J. C. 2 1988 The numerical analysis of ordinary differential equations. Runge-Kutta and general linear methods. Zbl 0616.65072Butcher, J. C. 562 1987 The equivalence of algebraic stability and AN-stability. Zbl 0637.65083Butcher, J. C. 14 1987 ...and 38 more Documents all cited Publications top 5 cited Publications all top 5 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 all top 5 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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.