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 |
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Pages (from-to) | 441-452 |
Number of pages | 12 |
Journal | Applications of Mathematics |
Volume | 59 |
Issue number | 4 |
DOIs | |
Publication status | Published - Aug 2014 |
Externally published | Yes |
Keywords
- Sinc-Galerkin method
- advection-diffusion equation
- numerical solution
ASJC Scopus subject areas
- Applied Mathematics