Numerical solutions of the coupled nonlinear Klein--Gordon equations by trigonometric integrator pseudospectral discretization

TL;DR

This paper introduces a pseudospectral and trigonometric integrator-based numerical scheme for solving coupled nonlinear Klein--Gordon equations, demonstrating high accuracy, stability, and efficiency through various tests.

Contribution

It presents a novel combination of pseudospectral spatial discretization with trigonometric time integration for Klein--Gordon equations.

Findings

High accuracy in numerical solutions

Stable under various test conditions

Efficient for high-resolution simulations

Abstract

A scheme stemming from the use of pseudospectral approximations to spatial derivatives followed by a time integrator based on trigonometric polynomials is proposed for the numerical solutions of the coupled nonlinear Klein--Gordon equations. Numerical tests on one- and three-coupled Klein--Gordon equations are presented, which are geared towards understanding the accuracy and stability, and demonstrating the efficiency and high resolution capacity in application.