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A numerical solution of the sine-Gordon equation using the modified decomposition method. (English) Zbl 1022.65114

Summary: The decomposition method for solving the sine-Gordon equation has been implemented. By using a number of initial values, the explicit and numerical solutions of the equation are calculated in the form of convergent power series with easily computable components. The present method performs extremely well in terms of accuracy, efficiency, simplicity, stability and reliability.

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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