Strong stability preserving hybrid methods

Authors:
Chengming Huang
Affiliations:
Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 17
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Abstract

This paper is concerned with the strong stability preserving (SSP) time discretizations for semi-discrete systems, obtained from applying the method of lines to time-dependent partial differential equations. We focus on the construction of explicit hybrid methods with nonnegative coefficients, which are a class of multistep methods incorporating a function evaluation at an off-step point. A series of new SSP methods are found. Among them, the low order methods are more efficient than some well known SSP Runge-Kutta or linear multistep methods. In particular, we present some fifth to seventh order methods with nonnegative coefficients, which have healthy CFL coefficients. Finally, some numerical experiments on the Burgers equation are given.