FITTED COMPUTATIONAL METHOD FOR CONVECTION DOMINATED DIFFUSION EQUATIONS WITH SHIFT ARGUMENTS

FITTED COMPUTATIONAL METHOD FOR CONVECTION DOMINATED DIFFUSION EQUATIONS WITH SHIFT ARGUMENTS

M. M. Woldaregay

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Abstract

A time dependent singularly perturbed convection di usion equation involv- ing shift parameters are considered. The terms containing the shifts are treated using Taylor series approximation up to second order terms. Classical numerical methods de- veloped for solving regular problems fail to give good approximate solution and become unstable while applied for the considered problem. In this paper, numerical scheme is developed using  -method for semi-discretizing in time derivative; in spatial discrtization  tted operator  nite di erence method is applied by inducing exponential  tting param- eter. To accelerate the convergence of the scheme, Richardson extrapolation technique is applied in spatial discretization. Existence of unique discrete solution is guaranteed by establishing the discrete comparison principle. The proposed scheme is stable for all values of the perturbation parameter. A uniformly convergent solution is obtained by Richardson extrapolation method which provides second order accuracy under some condition. Test examples are considered for validating the theoretical results numerically.

Keywords

Exponentially  tted scheme, Richardson extrapolation, convection domi- nated, uniform convergence.