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Rational approximation solution of the fractional Sharma-Tasso-Olever equation. (English) Zbl 1157.65074
Summary: We implement relatively new analytical techniques, the variational iteration method, the Adomian decomposition method and the homotopy perturbation method, for obtaining a rational approximation solution of the fractional Sharma-Tasso-Olever equation. The three methods in applied mathematics can be used as alternative methods for obtaining an analytic and approximate solution for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The numerical results demonstrate the significant features, efficiency and reliability of the three approaches.
MSC:
65R20Integral equations (numerical methods)
26A33Fractional derivatives and integrals (real functions)
45K05Integro-partial differential equations
45G10Nonsingular nonlinear integral equations
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations