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

Autor:	Runjie Zhang, Jinwei Fang
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Degasperis-Procesi equation strang splitting method convergence analysis lie derivative Mathematics QA1-939
Zdroj:	Axioms, Vol 12, Iss 10, p 946 (2023)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms12100946
Popis:	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.
Databáze:	Directory of Open Access Journals
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