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Variable coefficient a-stable explicit Runge-Kutta methods

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Abstract

The explicit Runge-Kutta methods possessing extended stability regions have already been discussed by many authors including van der Houwen [6]. It is the purpose of the present paper to derive a class of variable coefficients A-stable explicit Runge-Kutta methods. Some numerical tests justifying the results are given.

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References

  1. A.I. Johnson and J.R. Barney, Numerical solution of large systems of stiff ordinary differential equations in a modular framework. Numerical Methods for Differential Systems (eds. L. Lapidus and W. E. Schiesser), Academic Press INC., 1976, 97–124

  2. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations, John Wiley and Sons, 1987.

  3. T.E. Hull, W.H. Enright and A.E. Sedgwick, Memorandum on methods for stiff systems of ordinary differential equations. Department of Computer Science, University of Toronto, 1972.

  4. M. Nakashima, On the Stability of Variable-Formula Explicit Pseudo Runge-Kutta Method. Intern. Conf. at Benin Univ., 1992.

  5. M. Nakashima, Variable-coefficient A-stable explicit Runge-Kutta methods. Kokyuroku, Kyoto Univ.,841, 175–182.

  6. P.J. van der Houwen, Construction of Integration Formulas for Initial Value Problems. North-Holland, Amsterdam, 1977.

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  7. P.J. van der Houwen, On the time integration of parabolic differential equations. Lecture Notes in Mathematics912, Springer, 1982, 157–168.

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Correspondence to Masaharu Nakashima.

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Nakashima, M. Variable coefficient a-stable explicit Runge-Kutta methods. Japan J. Indust. Appl. Math. 12, 285–308 (1995). https://doi.org/10.1007/BF03167292

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  • DOI: https://doi.org/10.1007/BF03167292

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