An efficient hybrid numerical method based on an additive scheme for solving coupled systems of singularly perturbed linear parabolic problems |
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Authors: | Sunil Kumar Kuldeep Higinio Ramos Joginder Singh |
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Affiliation: | 1. Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi, Uttar Pradesh, India;2. Scientific Computing Group, Universidad de Salamanca, Salamanca, Spain |
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Abstract: | We construct an efficient hybrid numerical method for solving coupled systems of singularly perturbed linear parabolic problems of reaction-diffusion type. The discretization of the coupled system is based on the use of an additive or splitting scheme on a uniform mesh in time and a hybrid scheme on a layer-adapted mesh in space. It is proven that the developed numerical method is uniformly convergent of first order in time and third order in space. The purpose of the additive scheme is to decouple the components of the vector approximate solution at each time step and thus make the computation more efficient. The numerical results confirm the theoretical convergence result and illustrate the efficiency of the proposed strategy. |
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Keywords: | additive scheme generalized Shishkin mesh hybrid scheme singularly perturbed parabolic problem uniform convergence |
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