Error estimates in the energy space for a Gautschi-type integrator spectral discretization for the coupled nonlinear Klein–Gordon equations

We propose and analyze an efficient and accurate numerical method for solving the coupled nonlinear Klein–Gordon equations. The method is based on the application of a Gautschi-type exponential integrator in time combined with sine spectral discretization in space. The main results achieved in this paper are the rigorous error estimates in the energy space H1×H1H1×H1 for the proposed scheme. Numerical tests are reported and agree with the error estimates quite well.