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A computational approach to the wave equations: an application of the decomposition method. (English) Zbl 1058.65112
Summary: The authors study an analytic solution and a reliable numerical approximation of linear and nonlinear wave equations by using the Adomian decomposition method. The solution is calculated in the form of a series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-cancelling “noise terms” where the sum of the components vanishes in the limit. Several linear or nonlinear partial differential equations are considered and their numerical approximate solutions are compared with its numerical analytic solutions by applying the Adomian decomposition method and using a computer algebraic system (MATLAB). The numerical results show the effectiveness of the method for these types of equations.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
35L05 Wave equation
Software:
Matlab
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References:
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