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The purpose of this paper is to present an approach capable of solving Burgers' equation. Diagonal Padé approximation with a factorization scheme is applied to find numerical solutions of the one‐dimensional Burgers' equation by presenting explicit factoring the polynomials of the approximation. The numerical results obtained by this approach, for various values of viscosity, have been compared with the exact solution and are found to be in good agreement with each other.

In this paper, factorized diagonal Padé approach is applied to solve Burgers' equation. In this method, Burgers' equation is reduced to a system of ordinary differential equations and is solved piecewise analytically to obtain the solution of the problem.

The results of proposed approach show that when the obtained results are compared to similar methods, this approach gives better accuracy. Also, the graphs with small ν values satisfy the physical properties of the problem; therefore, the approach is promising for nonlinear problems.

The authors' experiments show that the applied method worked fine with Burgers' equation and they hope to extend it to some other nonlinear problems.

The proposed method is easy to implement and the given algorithm is easy to use, even for non experts. The approach is flexible to use high order Padé approximants.

In the approach described in the paper, Padé approximation is calculated in a different manner than the classical approach.

This paper aims to apply He's homotopy perturbation method (HPM) to obtain solitary solutions for the nonlinear dispersive equations with fractional time derivatives.

The authors choose as an example the nonlinear dispersive and equations with fractional time derivatives to illustrate the validity and the advantages of the proposed method.

The paper extends the application of the HPM to obtain analytic and approximate solutions to the nonlinear dispersive equations with fractional time derivatives.

This paper extends the HPM to the equation with fractional time derivative.