Abstract
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.
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Acknowledgments
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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Rao, S.C.S., Srivastava, V. Parameter-Robust Numerical Method for Time-Dependent Weakly Coupled Linear System of Singularly Perturbed Convection-Diffusion Equations. Differ Equ Dyn Syst 25, 301–325 (2017). https://doi.org/10.1007/s12591-016-0282-1
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DOI: https://doi.org/10.1007/s12591-016-0282-1
Keywords
- Time-dependent convection-diffusion problems
- Weakly coupled systems
- Shishkin mesh
- Backward Euler method
- HODIE scheme
- Parameter-uniform convergence