Work

Error Estimates of Time-Splitting Schemes for Nonlinear Klein–Gordon Equation with Rough Data

Year: 2026

Type: article

Abstract: . In this work, we consider the convergence analysis of time-splitting schemes for the nonlinear Klein–Gordon/wave equation under rough initial data. The optimal error bounds of the Lie splitting and the Strang splitting are established with sharp dependence on the regularity index of the solution from a wide range that is approaching the lower bound for well-posedness. Particularly for very rough data, the technique of discrete Bourgain space is utilized and developed, which can apply for general second-order wave models. Numerical verifications are provided.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/25m1743296

Authors: Lun Ji, Xiaofei Zhao

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, Wuhan University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1079102649, G659938121