A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problems with Discontinuous Convection Coefficient and Source Terms

• Published in: Differential equations and dynamical systems Vol. 27; no. 1-3; pp. 91 - 112
• Main Authors: Chandru, M., Prabha, T., Das, P., Shanthi, V.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.01.2019; Springer Nature B.V
• Subjects: Coefficients; Computer Science; Convection; Discontinuity; Engineering; Mathematics; Mathematics and Statistics; Numerical analysis; Numerical methods; Original Research; Parameters; Partial differential equations; Parabolic partial differential equation; 35K20; Initial boundary value problem; 35K51; Singular perturbation; Reaction-convection-diffusion; 65M06; Boundary and interior layers; Two-parameter problem; 35G05; 35G16; Parameter uniform numerical method; Time dependent problem; 65M50; 65M12
• ISSN: 0971-3514; 0974-6870
• DOI: 10.1007/s12591-017-0385-3

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.