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A collocation method for generalized nonlinear Klein-Gordon equation. (English) Zbl 1300.65072
Summary: In this paper, we propose a collocation method for an initial-boundary value problem of the generalized nonlinear Klein-Gordon equation. It possesses the spectral accuracy in both space and time directions. The numerical results indicate the high accuracy and the stability of long-time calculation of suggested algorithm, even for moderate mode in spatial approximation and big time step sizes. The main idea and techniques developed in this work provide an efficient framework for the collocation method of various nonlinear problems.

##### MSC:
 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q40 PDEs in connection with quantum mechanics 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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