Abstract
A new implicit integration method is presented which can efficiently be applied in the solution of (stiff) differential equations. The given formulas are of a modified implicit Runge-Kutta type and areA-stable. They may containA-stable embedded methods for error estimation and step-size control.
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References
J. C. Butcher,Implicit Runge-Kutta processes, Math. Comp. 18 (1964), 50–64.
E. Hairer et al.,On the Butcher group and general multivalue methods, Computing 13 (1974), 1–15.
E. Hairer et al.,Multistep-multistage-multiderivative methods for ordinary differential equations, Computing 11 (1973), 287–303.
B. Lindberg,A stiff system package based on the implicit midpoint method with smoothing and extrapolation, InStiff Differential Systems, Ed. R. A. Willoughby, Plenum Press, New York.
D. A. Calahan,A stable, accurate method of numerical integration for nonlinear systems, Proc. IEEE, 1968, p. 744.
K. S. Kunz,Numerical Analysis, McGraw-Hill, New York, 1957, p. 206.
B. L. Ehle,High order A-stable methods for the numerical solution of systems of D.E.'s, BIT 8 (1968), 276–278.
K. Burrage,A special family of Runge-Kutta methods for solving stiff differential equations, BIT 18 (1978), 22–41.
S. P. Nørsett,Runge-Kutta methods with a multiple real eigenvalue only, BIT 16 (1976), 388–393.
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van Bokhoven, W.M.G. Efficient higher order implicit one-step methods for integration of stiff differential equations. BIT 20, 34–43 (1980). https://doi.org/10.1007/BF01933583
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DOI: https://doi.org/10.1007/BF01933583