Summary
A single step process of Runge-Rutta type is examined for a linear differential equation of ordern. Conditions are derived which constrain the parameters of the process and which are necessary to give methods of specified order. A simple set of sufficient conditions is obtained.
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References
Butcher, J. C.: Coefficients for the study of Runge-Kutta integration processes. J. Aust. Math. Soc.3, 185–201 (1963).
— Implicit Runge-Kutta processes. Maths. of Comp.18, 50–64 (1964).
— On the convergence of numerical solutions to ordinary differential equations. Maths. of Comp.20, 1–10 (1966).
Henrici, P.: Discrete variable methods for ordinary differential equations. p. 66–68. New York: Wiley & Sons 1962.
Ince, E. L.: Ordinary differential equations, P. 73–75. New York: Dover Publ. 1956.
Zurmühl, R.: Runge-Kutta-Verfahren zur numerischen Integration von Differentialgleichungenn-ter Ordnung. Z. Angew. Math. Mech.28, 173–182 (1948).
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Cooper, G.J., Gal, E. Single step methods for linear differential equations. Numer. Math. 10, 307–315 (1967). https://doi.org/10.1007/BF02162029
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DOI: https://doi.org/10.1007/BF02162029