Numerical Solution of the Burgers' Equation Based on Sinc Method

Theory of Approximation and Applications

مقاله 3، دوره 13، شماره 1، مرداد 2019، صفحه 27-42   

نوع مقاله: Research Articles

نویسندگان

Ghasem Kazemi Gelian^{* 1}؛ Mohammad Ali Fariborzi Araghi²

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

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

چکیده

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

کلیدواژه‌ها

Burgers' Equation‎؛ ‎Sinc method‎؛ ‎Single‎ ‎Exponential Transformation

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