Additive Runge-Kutta methods for the resolution of linear parabolic problems

Authors:
B. Bujanda;J. C. Jorge
Affiliations:
Departmento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain;Departamento de Mathemática e Informática, Universidad Pública de Navarra, Edificio Los Acebos, Campus Arrosadía s/n, 31006 Pamplona, Spain
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

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Abstract

We study the consistency for general additive Runge-Kutta methods in the integration of linear nonhomogeneous problems, obtaining necessary and sufficient conditions of order p, for arbitrary values of p. We use this result joined to some A-stability conditions for developing a third order additive Runge-Kutta method of type fractional steps and we show its efficiency in the numerical integration of a two-dimensional evolutionary convection-diffusion problem.