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An Exponentially Fitted Numerical Scheme via Domain Decomposition for Solving Singularly Perturbed Differential Equations with Large Negative Shift

Author

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  • Ababi Hailu Ejere
  • Gemechis File Duressa
  • Mesfin Mekuria Woldaregay
  • Tekle Gemechu Dinka
  • Stanislaw Migorski

Abstract

In this study, we focus on the formulation and analysis of an exponentially fitted numerical scheme by decomposing the domain into subdomains to solve singularly perturbed differential equations with large negative shift. The solution of problem exhibits twin boundary layers due to the presence of the perturbation parameter and strong interior layer due to the large negative shift. The original domain is divided into six subdomains, such as two boundary layer regions, two interior (interfacing) layer regions, and two regular regions. Constructing an exponentially fitted numerical scheme on each boundary and interior layer subdomains and combining with the solutions on the regular subdomains, we obtain a second order ε-uniformly convergent numerical scheme. To demonstrate the theoretical results, numerical examples are provided and analyzed.

Suggested Citation

  • Ababi Hailu Ejere & Gemechis File Duressa & Mesfin Mekuria Woldaregay & Tekle Gemechu Dinka & Stanislaw Migorski, 2022. "An Exponentially Fitted Numerical Scheme via Domain Decomposition for Solving Singularly Perturbed Differential Equations with Large Negative Shift," Journal of Mathematics, Hindawi, vol. 2022, pages 1-13, June.
    • Handle: RePEc:hin:jjmath:7974134
    DOI: 10.1155/2022/7974134
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    Cited by:

    1. Gemechis File Duressa & Imiru Takele Daba & Chernet Tuge Deressa, 2023. "A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations," Mathematics, MDPI, vol. 11(5), pages 1-16, February.

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