A Robust numerical approach for singularly perturbed time delayed parabolic partial differential equations |
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Authors: | Aditya Kaushik Manju Sharma |
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Institution: | 1. Department of Mathematics DDE, Kurukshetra University, Kurukshetra, Haryana, India 2. Department of Applied Sciences, University Institute of Engineering and Technology, Kurukshetra University, Kurukshetra, Haryana, India
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Abstract: | We consider the numerical solution of a initial boundary value problem with a time delay. The problem under consideration
is singularly perturbed from the mathematical perspective. Assuming that the coefficients of the differential equation are
smooth, we construct and analyze the finite difference method whose solutions converge pointwise at all points of the domain
independently of the singular perturbation parameter. The method permits its extension to the case of adaptive meshes, which
may be used to improve the solution. Numerical examples are presented to demonstrate the effectiveness of the method. The
convergence obtained in practice satisfies the theoretical predictions. |
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Keywords: | |
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