Work

High-order uniformly accurate time integrators for semilinear wave equations of Klein–Gordon type in the non-relativistic limit

Year: 2025

Type: article

Abstract: We introduce a family of high-order time semi-discretizations for semilinear wave equations of Klein–Gordon type with arbitrary smooth nonlinearities that are uniformly accurate in the non-relativistic limit where the speed of light goes to infinity. Our schemes do not require pre-computations that are specific to the nonlinearity and have no restrictions in step size. Instead, they rely upon a general oscillatory quadrature rule based on Gauss summation which was previously developed by the authors.

Source: BIT Numerical Mathematics

DOI: 10.1007/s10543-025-01084-7

Authors: Haidar Mohamad, Marcel Oliver

Institution: Constructor University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Deutsche Forschungsgemeinschaft