Abstract
A space-time spectral method for the nonlinear Klein-Gordon equation is proposed. We use the Legendre-Galerkin method in space and Legendre-Petrov-Galerkin method in time. The nonlinear term in the equation is dealt with the Chebyshev spectral collocation method. The scheme results in a simple algebraic system by choosing appropriate basis functions. The stability and the optimal error estimates in L2-norm for the single and multiple interval methods are given. Numerical experiments are shown confirming the theoretical results.
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