We propose to derive the explicit multistage methods of the Runge-Kutta type for ordinary differential equations (ODEs) with the aid of the expansion of grid functions into the Lagrange-Burmann series. New explicit first- and second-order methods are derived, which are applied to the numerical integration of the Cauchy problem for a moderately stiff ODE system. It turns out that the L 2 norm of the error of the solution obtained by the new numerical second-order method is 50 times smaller than in the case of the classical second-order Runge-Kutta method. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Vorozhtsov, E. V. (2010). Derivation of explicit difference schemes for ordinary differential equations with the aid of Lagrange-Burmann expansions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6244 LNCS, pp. 250–266). https://doi.org/10.1007/978-3-642-15274-0_23
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