Geodesic
Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
Applications of Mathematics, Tome 59 (2014) no. 4, pp. 441-452

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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.
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.
DOI : 10.1007/s10492-014-0065-3
Classification : 35A01, 35B25, 35F05, 35K57, 35L65, 35Q53, 65M70, 65T60
Keywords: Sinc-Galerkin method; advection-diffusion equation; numerical solution 
Al-Khaled, Kamel. Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods. Applications of Mathematics, Tome 59 (2014) no. 4, pp. 441-452. doi: 10.1007/s10492-014-0065-3
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     title = {Existence of solutions to nonlinear advection-diffusion equation applied to {Burgers'} equation using {Sinc} methods},
     journal = {Applications of Mathematics},
     pages = {441--452},
     year = {2014},
     volume = {59},
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     zbl = {06362237},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0065-3/}
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