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Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions

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  • Kumar, Sunil
  • Sumit,
  • Ramos, Higinio

Abstract

In this work we develop a parameter-uniform numerical method on equidistributed meshes for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions. The discretization consists of a modified Euler scheme in time, a central difference scheme in space, and a special finite difference scheme for the Robin boundary conditions. A uniform mesh is used in the time direction while the mesh in the space direction is generated via the equidistribution of a suitably chosen monitor function. We discuss error analysis and prove that the method is parameter-uniformly convergent of order two in space and order one in time. To support the theoretical result, some numerical experiments are performed.

Suggested Citation

  • Kumar, Sunil & Sumit, & Ramos, Higinio, 2021. "Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306305
    DOI: 10.1016/j.amc.2020.125677
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    References listed on IDEAS

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    1. Avudai Selvi, P. & Ramanujam, N., 2017. "A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 101-115.
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    Cited by:

    1. Kumar, Sunil & Sumit, & Vigo-Aguiar, Jesus, 2022. "A high order convergent numerical method for singularly perturbed time dependent problems using mesh equidistribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 287-306.

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