In this paper, a Kawahara equation is solved by using the Adomian’s decompositionmethod, modiï¬ed Adomian’s decomposition method, variational iteration method,modiï¬ed variational iteration method, homotopy perturbation method, modiï¬ed homotopyperturbation method and homotopy analysis method. The approximate solution of thisequation is calculated in the form of series which its components are computed byapplying a recursive relation. The existence and uniqueness of the solution and theconvergence of the proposed methods are proved. A numerical example is studied todemonstrate the accuracy of the presented methods.
Key words: Kawahara equation, Adomian decomposition method (ADM), modiï¬edAdomian decomposition method (MADM), variational iteration method (VIM), modiï¬edvariational iteration method (MVIM), homotopy perturbation method (HPM), modiï¬edhomotopy perturbation method (MHPM), homotopy analysis method (HAM).
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