Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods

Kamel Al-Khaled

Research output: Contribution to journalArticle

Abstract

This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution is shown to converge to the exact solution at an exponential rate. A numerical example is given to illustrate the accuracy of the method.

Original languageEnglish
Pages (from-to)441-452
Number of pages12
JournalApplications of Mathematics
Volume59
Issue number4
DOIs
Publication statusPublished - 2014

Keywords

  • advection-diffusion equation
  • numerical solution
  • Sinc-Galerkin method

ASJC Scopus subject areas

  • Applied Mathematics

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