Convergence Analysis of the Strang Splitting Method for the Degasperis-Procesi Equation

Abstract

This article is concerned with the convergence properties of the Strang splitting method for the Degasperis-Procesi equation, which models shallow water dynamics. The challenges of analyzing splitting methods for this equation lie in the fact that the involved suboperators are both nonlinear. In this paper, instead of building the second order convergence in L2 for the proposed method directly, we first show that the Strang splitting method has first order convergence in H2. In the analysis, the Lie derivative bounds for the local errors are crucial. The obtained first order convergence result provides the H2 boundedness of the approximate solutions, thereby enabling us to subsequently establish the second order convergence in L2 for the Strang splitting method.