Preprint 1996-036

Convergence Analysis for Operator Splitting Methods to Conservation Laws with Stiff Source Terms

Abstract: We analyze the order of convergence for operator splitting methods applied to conservation laws with stiff source terms. We suppose that the source term $q(u)$ is dissipative. It is proved that the $L^1$ error introduced by the time-splitting can be bounded by $O( \D t \Vert q(u_0 )\Vert_{L^1(\R)} )$, which is an improvement of the $O( Q \D t )$ upper bound, where $\D t$ is the splitting time step, $Q$ is the Lipschitz constant of $q$ or $Q= \max_{u} \vert q'(u) \vert$ in case $q$ is smooth. We also propose a non-uniform temporal mesh which can eliminate the effect of the initial layer introduced by the stiff source term.

Paper:

Available as PostScript

Title:

Convergence Analysis for Operator Splitting Methods to Conservation Laws with Stiff Source Terms

Author(s):

Tao Tang, mailto:tangtao@cs.sfu.ca

Publishing information:

Submitted.

Submitted by:

mailto:tangtao@cs.sfu.ca October 12 1996.