## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014 (2014), Article ID 598432, 15 pages.

### On the Numerical Solution of One-Dimensional Nonlinear Nonhomogeneous Burgers’ Equation

Maryam Sarboland and Azim Aminataei

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#### Abstract

The nonlinear Burgers’ equation is a simple form of Navier-Stocks equation. The nonlinear nature of Burgers’ equation has been exploited as a useful prototype differential equation for modeling many phenomena. This paper proposes two meshfree methods for solving the one-dimensional nonlinear nonhomogeneous Burgers’ equation. These methods are based on the multiquadric (MQ) quasi-interpolation operator ${\mathcal{L}}_{{\mathcal{W}}_{2}}$ and direct and indirect radial basis function networks (RBFNs) schemes. In the present schemes, the Taylors series expansion is used to discretize the temporal derivative and the quasi-interpolation is used to approximate the solution function and its spatial derivatives. In order to show the efficiency of the present methods, several experiments are considered. Our numerical solutions are compared with the analytical solutions as well as the results of other numerical schemes. Furthermore, the stability analysis of the methods is surveyed. It can be easily seen that the proposed methods are efficient, robust, and reliable for solving Burgers’ equation.

#### Article information

**Source**

J. Appl. Math., Volume 2014 (2014), Article ID 598432, 15 pages.

**Dates**

First available in Project Euclid: 2 March 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1425305684

**Digital Object Identifier**

doi:10.1155/2014/598432

**Mathematical Reviews number (MathSciNet)**

MR3198390

#### Citation

Sarboland, Maryam; Aminataei, Azim. On the Numerical Solution of One-Dimensional Nonlinear Nonhomogeneous Burgers’ Equation. J. Appl. Math. 2014 (2014), Article ID 598432, 15 pages. doi:10.1155/2014/598432. https://projecteuclid.org/euclid.jam/1425305684

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