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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015, Tamilnadu, India

    M. Chandru, T. Prabha & V. Shanthi

  2. Department of Mathematics, Vignan’s University, Vadlamudi, Andhra Pradesh, India

    M. Chandru

  3. Department of Mathematics, Indian Institute of Technology Patna, Patna, 801 103, Bihar, India

    P. Das

Authors
  1. M. Chandru
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  2. T. Prabha
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  3. P. Das
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  4. V. Shanthi
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Corresponding author

Correspondence to P. Das.

Additional information

The first and fourth authors wish to thank Department of Science and Technology(SERB), Government of India, New Delhi for financial support of project SR/FTP/MS-039/2012.

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Chandru, M., Prabha, T., Das, P. et al. A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problems with Discontinuous Convection Coefficient and Source Terms. Differ Equ Dyn Syst 27, 91–112 (2019). https://doi.org/10.1007/s12591-017-0385-3

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  • DOI: https://doi.org/10.1007/s12591-017-0385-3

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