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

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Listed:
  • Ababi Hailu Ejere
  • Gemechis File Duressa
  • Mesfin Mekuria Woldaregay
  • Tekle Gemechu Dinka

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, 2022. "An Exponentially Fitted Numerical Scheme via Domain Decomposition for Solving Singularly Perturbed Differential Equations with Large Negative Shift," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:7974134
    DOI: 10.1155/2022/7974134
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    References listed on IDEAS

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    1. Habtamu Garoma Debela & Solomon Bati Kejela & Ayana Deressa Negassa, 2020. "Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations," International Journal of Differential Equations, Hindawi, vol. 2020, pages 1-13, June.
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    Cited by:

    1. Amare Worku Demsie & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "An Exponentially Fitted Upwind Scheme for Singularly Perturbed Differential Equations With Mixed Shift Parameters," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    2. Mulunesh Amsalu Ayele & Awoke Andargie Tiruneh & Getachew Adamu Derese, 2022. "Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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