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An efficient numerical algorithm for the fractional Drinfeld-Sokolov-Wilson equation. (English) Zbl 1427.65324
Summary: The fundamental purpose of the present paper is to apply an effective numerical algorithm based on the mixture of homotopy analysis technique, Sumudu transform approach and homotopy polynomials to obtain the approximate solution of a nonlinear fractional Drinfeld-Sokolov-Wilson equation. The nonlinear Drinfeld-Sokolov-Wilson equation naturally occurs in dispersive water waves. The uniqueness and convergence analysis are shown for the suggested technique. The convergence of the solution is fixed and managed by auxiliary parameter $$\hslash$$. The numerical results are shown graphically. Results obtained by the application of the technique disclose that the suggested scheme is very accurate, flexible, effective and simple to use.

##### MSC:
 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 44A10 Laplace transform
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