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A scheme stemming from the use of pseudospectral approximations to spatialderivatives followed by a time integrator based on trigonometric polynomials isproposed for the numerical solutions of the coupled nonlinear Klein--Gordonequations. Numerical tests on one- and three-coupled Klein--Gordon equationsare presented, which are geared towards understanding the accuracy andstability, and demonstrating the efficiency and high resolution capacity inapplication.

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