A trigonometric integrator pseudospectral discretization for the N‐coupled nonlinear Klein–Gordon equations

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 N‐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 illustrating its efficiency and high resolution capacity in applications.