Article
MSC:
35A01,
35B25,
35F05,
35K57,
35L65,
35Q53,
65M70,
65T60 | MR 3233553 | Zbl 06362237 | DOI: 10.1007/s10492-014-0065-3
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Keywords:
Sinc-Galerkin method; advection-diffusion equation; numerical solution
Sinc-Galerkin method; advection-diffusion equation; numerical solution
Summary:
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.
References:
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