A reliable technique for solving the wave equation in an infinite one-dimensional medium. (English) Zbl 0942.65107

Wazwaz, Abdul-Majid

Appl. Math. Comput. 92, No. 1, 1-7 (1998).

Summary: The initial value problem of the one-dimensional wave equation, where the domain of the space variable is unbounded, will be handled by using the reliable decomposition method. The solution is obtained in the form of a rapid convergent power series with elegantly computable terms. Comparing the decomposition method we used with several other methods that have been advanced for solving this model, shows that the new technique is reliable, powerful and promising.

MSC:

65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35L05	Wave equation
65M12	Stability and convergence of numerical methods 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

Keywords:

convergence; infinite domain; D’Alembert formula; Adomian decomposition method; initial value problem; wave equation

References:

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