High order parameter-robust numerical method for singularly perturbed reaction-diffusion problems |
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Authors: | Mukesh Kumar |
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Institution: | Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India |
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Abstract: | We present a high order parameter-robust finite difference method for singularly perturbed reaction-diffusion problems. The problem is discretized using a suitable combination of fourth order compact difference scheme and central difference scheme on generalized Shishkin mesh. The convergence analysis is given and the method is proved to be almost fourth order uniformly convergent in maximum norm with respect to singular perturbation parameter ε. Numerical experiments are conducted to demonstrate the theoretical results. |
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Keywords: | Singular perturbation problems Reaction-diffusion problems Hybrid scheme Generalized Shishkin mesh Parameter-robust convergence Pointwise error estimate Global error estimate |
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