TY - JOUR

T1 - Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods

AU - Al-Khaled, Kamel

PY - 2014/8

Y1 - 2014/8

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 - Sinc-Galerkin method

KW - advection-diffusion equation

KW - numerical solution

UR - http://www.scopus.com/inward/record.url?scp=84904735065&partnerID=8YFLogxK

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U2 - 10.1007/s10492-014-0065-3

DO - 10.1007/s10492-014-0065-3

M3 - Article

AN - SCOPUS:84904735065

VL - 59

SP - 441

EP - 452

JO - Applications of Mathematics

JF - Applications of Mathematics

SN - 0862-7940

IS - 4

ER -