A New Iteration Multivariate Pade´ Approximation Technique for Nonlinear Partial Differential Equations of Fractional Order

Abstract

In this paper, the Laplace transform, the New iteration method and the Multivariate Pade´ approximation technique are employed to solve nonlinear fractional partial differential equations whose fractional derivatives are described in the sense of Caputo. The Laplace transform is used to ”fully” determine the initial iteration value. The New iteration method gives a sequence of series solution which approximates the exact solution of the nonlinear equations. The Multivariate Pade´ approximation is used to accelerate the rate of convergence of solutions obtained by the New iteration method. Numerical illustrations were given to show the robustness, simplicity and efficacy of the approach. Also results obtained by the Multivariate Pade´ approximation were compared with the results obtained by the Adomian decomposition method.

Keywords: New iteration method, Laplace transform, Multivariate Pade´ approximations, nonlinear fractional partial differential equations, Exact solutions