Some new additive Runge-Kutta methods and their applications

Authors:
Hongyu Liu;Jun Zou
Affiliations:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We propose some new additive Runge-Kutta methods of orders ranging from 2 to 4 that may be used for solving some nonlinear system of ODEs, especially for the temporal discretization of some nonlinear systems of PDEs with constraints. Only linear ODEs or PDEs need to be solved at each time step with these new methods.