A numerical solution of the Klein-Gordon equation and convergence of the decomposition method. (English) Zbl 1084.65101

The authors use the Adomian decomposition method (ADM) for solving a nonlinear hyperbolic equation: the Klein-Gordon equation. The Adomian method allows to find the solution without discretization or linearization. The convergence is proved by using a result given by T. Mavoungou and Y. Cherruault [Kybernetes 21, No. 6, 13–25 (1992; Zl 0801.35007)]. Practically the solution is obtained with only initial conditions. Numerical results are given proving the efficacy of the ADM technique. It would be interesting to treat partial differential equations with both initial and boundary conditions.


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


Zbl 0801.35007
Full Text: DOI


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