Studies an analytic solution and a reliable numerical approximation of linear and non‐linear wave equations by using the Adomian decomposition method. The solution is calculated in the form of a series with easily computable components. The non‐homogeneous problem is quickly solved by observing the self‐cancelling “noise terms” where the sum of the components vanishes in the limit. Several linear or non‐linear 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.
Inc, M., Cherruault, Y. and Abbaoui, K. (2004), "A computational approach to the wave equations: An application of the decomposition method", Kybernetes, Vol. 33 No. 1, pp. 80-97. https://doi.org/10.1108/03684920410514535Download as .RIS
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