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Fitted Operator Method Using Multiple Fitting Factors for Two Parameters Singularly Perturbed Parabolic Problems

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  • Dagnachew Mengstie Tefera
  • Awoke Andargie Tiruneh
  • Getachew Adamu Derese
  • Nasser Hassen Sweilam

Abstract

In this paper, we produce ϵ,μ− uniform numerical method for a singularly perturbed parabolic differential equation with two parameters. To approximate the solution, we consider the implicit Euler method for time direction, the finite difference method for spatial direction on a uniform mesh, and the fitted operator method with multiple fitting factors. To accelerate the convergence of the method, the Richardson extrapolation method is applied. The results show that the proposed method is second-order convergent in both temporal and spatial directions. The convergence of the scheme is insensitive to the two perturbation parameters. Two model examples are considered to validate the applicability of the proposed method and produced more accurate results compared to some methods that appear in the literature. Matlab software is used to manipulate the results.

Suggested Citation

  • Dagnachew Mengstie Tefera & Awoke Andargie Tiruneh & Getachew Adamu Derese & Nasser Hassen Sweilam, 2022. "Fitted Operator Method Using Multiple Fitting Factors for Two Parameters Singularly Perturbed Parabolic Problems," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-10, July.
    • Handle: RePEc:hin:jnlmpe:6267522
    DOI: 10.1155/2022/6267522
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