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Sinc Approximation of Solution of Burgers' Equation with Discontinuous
Initial Condition

By

Kamel Al-Khaled

Department of Applied Mathematical Sciences

Jordan University of Science and Technology

Irbid 22110, Jordan
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\section{Abstract}

A numerical scheme using Sinc-Galerkin method is developed to approximate
the solution of the advection-diffusion equation

\[
u_t+uu_x=\epsilon \,u_{xx}
\]

with discontinuous initial condition, the discontinuity being at $x=0$. The
main idea is to replace differential and integral equations by their Sinc
approximation. The error in the approximation of the solution is shown to
converge at an exponential rate. A numerical example is given to illustrate
the accuracy of the method.

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