B-convergence of general linear methods for stiff problems

Authors:
Chengming Huang;Qianshun Chang;Aiguo Xiao
Affiliations:
Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China;Institute of Applied Mathematics, The Chinese Academy of Sciences, P.O. Box 2734, Beijing 100080, China;Department of Mathematics, Xiangtan University, Hunan 411105, China
Venue:
Applied Numerical Mathematics
Year:
2003

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Abstract

This paper is concerned with the numerical solution of stiff initial value problems for systems of ordinary differential equations by general linear methods. We prove that algebraic stability together with strict stability at infinity implies B-convergence for strictly dissipative systems and that the order of B-convergence of a method is equal to the generalized stage order, where the generalized stage order is not less than the stage order, which extends the relevant results on Runge-Kutta methods. As applications of this result, B-convergence results of some classes of multistep Runge-Kutta methods are obtained.