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 language | English |
|---|---|
| Pages (from-to) | 441-452 |
| Number of pages | 12 |
| Journal | Applications of Mathematics |
| Volume | 59 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2014 |
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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 journal › Article
}
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 -