Parameter-Robust Numerical Method for Time-Dependent Weakly Coupled Linear System of Singularly Perturbed Convection-Diffusion Equations
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We present a parameter-robust numerical method for a time-dependent weakly coupled linear system of singularly perturbed convection-diffusion equations. A small perturbation parameter multiplies the second order spatial derivative in all the equations. The proposed numerical method uses backward Euler method in time direction on an uniform mesh together with a suitable combination of HODIE scheme and the central difference scheme in spatial direction on a Shishkin mesh. It is proved that the numerical method is parameter-robust of first order in time and almost second order in space. Numerical results are given in support of theoretical findings.
KeywordsTime-dependent convection-diffusion problems Weakly coupled systems Shishkin mesh Backward Euler method HODIE scheme Parameter-uniform convergence
Mathematics Subject Classification65M06 65M12 65M15
The authors gratefully acknowledge the valuable comments and suggestions from the anonymous referees. The research work of the second author is supported by Council of Scientific and Industrial Research, India.
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