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Parameter-uniform numerical method for a two-dimensional singularly perturbed convection–reaction–diffusion problem with interior and boundary layers

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  • Rao, S. Chandra Sekhara
  • Chaturvedi, Abhay Kumar

Abstract

We consider a two-dimensional singularly perturbed convection–reaction–diffusion problem that has discontinuities, along lines parallel to x- and y-axes, in the source term, as well as in the convection and reaction coefficients. The coefficient of the highest-order term is a small positive parameter denoted by ε. Due to the discontinuities, the solution exhibits layers in the interior of the domain, in addition to boundary layers. We propose a decomposition of the solution that yields sharp bounds on its derivatives. A finite difference scheme is constructed on an appropriate Shishkin mesh, and it is established that the computed solution is almost first-order, parameter-uniformly convergent. Numerical results are given to support the theoretical results.

Suggested Citation

  • Rao, S. Chandra Sekhara & Chaturvedi, Abhay Kumar, 2021. "Parameter-uniform numerical method for a two-dimensional singularly perturbed convection–reaction–diffusion problem with interior and boundary layers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 656-686.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:656-686
    DOI: 10.1016/j.matcom.2021.03.016
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    Cited by:

    1. Shiromani, Ram & Shanthi, Vembu & Ramos, Higinio, 2023. "A computational method for a two-parameter singularly perturbed elliptic problem with boundary and interior layers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 40-64.

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