Numerical solution of Burgers' equation with factorized diagonal Padé approximation

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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

Practical implications

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.

Originality/value

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

Citation

Altıparmak, K. and Öziş, T. (2011), "Numerical solution of Burgers' equation with factorized diagonal Padé approximation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 3, pp. 310-319. https://doi.org/10.1108/09615531111108486