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

Fingerprint

Sinc Method
Advection-diffusion Equation
Advection
Burgers Equation
Existence of Solutions
Nonlinear Equations
Galerkin methods
Galerkin Method
Numerical Scheme
Turbulence
Approximate Solution
Initial conditions
Exact Solution
Converge
Numerical Examples
Model

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods. / Al-Khaled, Kamel.

In: Applications of Mathematics, Vol. 59, No. 4, 2014, p. 441-452.

Research output: Contribution to journalArticle

@article{9dd149a73f6c4699ab6719932f47e974,
title = "Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods",
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.",
keywords = "advection-diffusion equation, numerical solution, Sinc-Galerkin method",
author = "Kamel Al-Khaled",
year = "2014",
doi = "10.1007/s10492-014-0065-3",
language = "English",
volume = "59",
pages = "441--452",
journal = "Applications of Mathematics",
issn = "0862-7940",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods

AU - Al-Khaled, Kamel

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - advection-diffusion equation

KW - numerical solution

KW - Sinc-Galerkin method

UR - http://www.scopus.com/inward/record.url?scp=84904735065&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904735065&partnerID=8YFLogxK

U2 - 10.1007/s10492-014-0065-3

DO - 10.1007/s10492-014-0065-3

M3 - Article

VL - 59

SP - 441

EP - 452

JO - Applications of Mathematics

JF - Applications of Mathematics

SN - 0862-7940

IS - 4

ER -