Abstract
A family of two-sided Runge—Kutta formulas accurate to sixth order is constructed for numerical solution of the Cauchy problem for second-order ordinary differential equations, which are solved for the highest derivative and have a sufficiently smooth right-hand side. Two-sided approximations to the sought solution are obtained after up to nine evaluations of the right-hand side of the differential equation in each integration step. The efficiency of the proposed formula is demonstrated in application to two test examples.
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References
N. S. Golovan', Construction of Two-Sided Runge—Kutta Approximations Accurate to Fifth Order [in Russian], Unpublished manuscript, VINITI 01.09.80, No. 3962, Moscow (1980).
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Additional information
Sumy Teachers' College. Kiev Teachers' College. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 45–51, 1989.
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Golovan’, N.S., Lyashchenko, N.Y. Two-sided Runge-Kutta method accurate to sixth order for second-order ordinary differential equations. J Math Sci 69, 1404–1409 (1994). https://doi.org/10.1007/BF01250583
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DOI: https://doi.org/10.1007/BF01250583