Convergence Analysis of the Strang Splitting Method for the Degasperis-Procesi Equation
Convergence Analysis of the Strang Splitting Method for the Degasperis-Procesi Equation
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DOI：
10.3390/axioms12100946
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发表时间：
2023-10
期刊：
影响因子：
2
通讯作者：
Runjie Zhang;Jinwei Fang
中科院分区：
文献类型：
--
作者：
Runjie Zhang;Jinwei Fang
本文研究了模拟浅水动力学的Degasperis-Procesi方程的斯特朗分裂方法的收敛性。分析该方程分裂方法的挑战在于所涉及的子算子都是非线性的。在本文中，而不是建立在L2的直接所提出的方法的二阶收敛，我们首先表明，斯特朗分裂方法在H2的一阶收敛。在分析中，局部误差的李导数界是关键。得到的一阶收敛结果提供了近似解的H2有界性，从而使我们能够随后建立斯特朗分裂方法在L2中的二阶收敛。
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.