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Burrage, Kevin

A special family of Runge-Kutta methods for solving stiff differential equations. (English) Zbl 0384.65034

BIT, Nord. Tidskr. Inf.-behandl. 18, 22-41 (1978).
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Cited in 72 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L07 Numerical investigation of stability of solutions to ordinary differential equations
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\textit{K. Burrage}, BIT, Nord. Tidskr. Inf.-behandl. 18, 22--41 (1978; Zbl 0384.65034)
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References:

[1] J. C. Butcher,Implicit Runge-Kutta Processes, Math. Comp. 18 (1964), 50–64. · Zbl 0123.11701
[2] J. C. Butcher,Chapter 5, Modern Numerical Methods for Ordinary Differential Equations, edited by G. Hall and J. M. Watt, Clarendon Press, Oxford 1976. · Zbl 0331.65045
[3] J. C. Butcher,On the Implementation of Runge-Kutta Methods, BIT 16 (1976), 237–240. · Zbl 0336.65037
[4] J. C. Butcher,A Transformed Implicit Runge-Kutta Method, Mathematics Department, University of Auckland, Report Series No. 111. · Zbl 0439.65057
[5] S. P. Nørsett,Multiple Padé approximations to the Exponential Function, Mathematics Department, University of Trondheim, Report No. 4/74.
[6] S. P. Nørsett,Semi-Explicit Runge-Kutta Methods, Mathematics Department, University of Trondheim, Report No. 6/74. · Zbl 0345.65036
[7] S. P. Nørsett,Runge-Kutta Methods with a multiple real eigenvalue only, BIT 16 (1976), 388–393. · Zbl 0345.65036
[8] S. P. Nørsett and A. Wolfbrandt,Attainable order of rational approximations to the exponential function with only real poles, BIT 17 (1977), 200–208. · Zbl 0361.41011
[9] J. V. Uspensky,Theory of Equations, McGraw-Hill, New York, 1948.
[10] J. H. Verner,Explicit Runge-Kutta Methods with Estimates of the Local Truncation Error, Mathematics Department, University of Auckland, Report Series No. 92. · Zbl 0403.65029
[11] A. Wolfbrandt,A Study of Rosenbrock Processes with respect to order conditions and Stiff Stability, Department of Computer Sciences, University of Göteborg, Sweden. · Zbl 0371.41007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.