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Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations

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  • Habtamu Garoma Debela
  • Solomon Bati Kejela
  • Ayana Deressa Negassa

Abstract

This paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. A fourth-order exponentially fitted numerical scheme on uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on four model examples. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnijde:5768323
    DOI: 10.1155/2020/5768323
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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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