Numerical Solution of the Burgers' Equation Based on Sinc Method

Document Type: Research Articles

Authors

1 Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran

2 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

Abstract

Burgers' equation arises in various areas of applied mathematics,‎
‎such as modeling of dynamics‎, ‎heat conduction‎, ‎and acoustic‎
‎waves‎ Also‎, ‎this equation has a large variety of applications in‎
‎the modeling of water in unsaturated soil‎, ‎dynamics of soil‎
‎water‎, ‎models of traffic‎, ‎turbulence and fluid flow‎, ‎mixing and‎
‎turbulent diffusion.

Many researchers tried to find analytic and numerical solutions of‎
‎ this equation by different methods.

Sinc method is a powerful numerical tool for finding fast and‎
‎accurate solution in various areas of problems.‎

In this paper‎, ‎numerical solution of Burgers' equation‎
‎is considered by applying Sinc method‎. ‎For this purpose‎, ‎we apply‎
‎Sinc method in cooperative with a classic finite difference‎
‎formula to‎ ‎Burgers'equation‎. ‎‎The purpose of this paper is to extend the application of the‎
‎sinc method for solving Burgers'equation by considering stability‎
‎analysis of the method.‎

Numerical examples are provided to verify the validity of proposed method

Keywords

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