Ordinary differential equations with the aid of lagrange-burmann expansions

Authors:
Evgenii V. Vorozhtsov
Affiliations:
Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia
Venue:
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Year:
2010

Citing 3
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Abstract

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 L2 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.