Numerical Solution of the Burgers' Equation Based on Sinc Method

Abstract

Burgers' equation arises in various areas of applied mathematics,‎<br />‎such as modeling of dynamics‎, ‎heat conduction‎, ‎and acoustic‎<br />‎waves‎ Also‎, ‎this equation has a large variety of applications in‎<br />‎the modeling of water in unsaturated soil‎, ‎dynamics of soil‎<br />‎water‎, ‎models of traffic‎, ‎turbulence and fluid flow‎, ‎mixing and‎<br />‎turbulent diffusion. <br /><br /><br />Many researchers tried to find analytic and numerical solutions of‎<br />‎ this equation by different methods.<br /><br />Sinc method is a powerful numerical tool for finding fast and‎<br />‎accurate solution in various areas of problems.‎<br /><br />In this paper‎, ‎numerical solution of Burgers' equation‎<br />‎is considered by applying Sinc method‎. ‎For this purpose‎, ‎we apply‎<br />‎Sinc method in cooperative with a classic finite difference‎<br />‎formula to‎ ‎Burgers'equation‎. ‎‎The purpose of this paper is to extend the application of the‎<br />‎sinc method for solving Burgers'equation by considering stability‎<br />‎analysis of the method.‎ <br /><br />Numerical examples are provided to verify the validity of proposed method