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

Kamel Al-Khaled

Applications of Mathematics (2014)

  • Volume: 59, Issue: 4, page 441-452
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Al-Khaled, Kamel. "Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods." Applications of Mathematics 59.4 (2014): 441-452. <http://eudml.org/doc/261941>.

@article{Al2014,
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.},
author = {Al-Khaled, Kamel},
journal = {Applications of Mathematics},
keywords = {Sinc-Galerkin method; advection-diffusion equation; numerical solution; Sinc-Galerkin method; advection-diffusion equation; numerical solution},
language = {eng},
number = {4},
pages = {441-452},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods},
url = {http://eudml.org/doc/261941},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Al-Khaled, Kamel
TI - Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 441
EP - 452
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.
LA - eng
KW - Sinc-Galerkin method; advection-diffusion equation; numerical solution; Sinc-Galerkin method; advection-diffusion equation; numerical solution
UR - http://eudml.org/doc/261941
ER -

References

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