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A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problems with Discontinuous Convection Coefficient and Source Terms
, T. Prabha, P. Das, V. Shanthi
Published in Springer (India) Private Ltd.
Volume: 27
Issue: 1-3
Pages: 91 - 112
In this article, a parameter uniform numerical method is developed for a two-parameter singularly perturbed parabolic partial differential equation with discontinuous convection coefficient and source term. The presence of perturbation parameter and the discontinuity in the convection coefficient and source term lead to the boundary and interior layers in the solution. On the spatial domain, an adaptive mesh is introduced before discretizing the continuous problem. The present method observes a uniform convergence in maximum norm which is almost first-order in space and time irrespective of the relation between convection and diffusion parameters. Numerical experiment is carried out to validate the present scheme. © 2017, Foundation for Scientific Research and Technological Innovation.
About the journal
JournalData powered by TypesetDifferential Equations and Dynamical Systems
PublisherData powered by TypesetSpringer (India) Private Ltd.