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

2025/02/24 by Lun Ji, Xiaofei Zhao, Ji, Lun +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Advanced Numerical Methods in Computational Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.1137/25m1743296

Abstract

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.

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