FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 4, PAGES 1131-1140

On symmetry of some Runge--Kutta methods

G. Yu. Kulikov

Abstract

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In the paper we investigate the property of symmetry for Runge--Kutta methods. We prove that methods possessing such property are fully implicit, and they can be constructed by the Gauss and Lobatto quadrature formulas. But only the Gauss formulas give algebraically stable Runge--Kutta methods.

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Last modified: February 13, 2001