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An Exponentially Fitted Upwind Scheme for Singularly Perturbed Differential Equations With Mixed Shift Parameters

Author

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  • Amare Worku Demsie
  • Awoke Andargie Tiruneh
  • Endalew Getnet Tsega

Abstract

This paper provides numerical solutions to a class of singularly perturbed differential–difference equations characterized by mixed shift parameters. The solutions of such problems exhibit sharp boundary layers near the endpoints of the spatial domain due to the presence of a small perturbation parameter ε(0

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:3048746
    DOI: 10.1155/jom/3048746
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    References listed on IDEAS

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    1. 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.
    2. Mesfin Mekuria Woldaregay & Gemechis File Duressa, 2021. "Uniformly Convergent Hybrid Numerical Method for Singularly Perturbed Delay Convection-Diffusion Problems," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-20, September.
    3. 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).
    4. Amare Worku Demsie & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "A Uniformly Convergent Scheme for Singularly Perturbed Unsteady Reaction–Diffusion Problems," Journal of Applied Mathematics, Hindawi, vol. 2025, pages 1-15, March.
    5. Tesfaye Aga Bullo, 2022. "Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    6. 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).
    7. Amare Worku Demsie & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "A Fitted Linear Multistep Approach for Singularly Perturbed Parabolic‐Type Reaction–Diffusion Problems Using Shishkin Meshes," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    8. Mulunesh Amsalu Ayele & Awoke Andargie Tiruneh & Getachew Adamu Derese & Serkan Araci, 2022. "Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, October.
    9. Awoke Andargie Tiruneh & Getachew Adamu Derese & Dagnachew Mengstie Tefera & Palle Kiran, 2022. "A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-11, July.
    10. Amare Worku Demsie & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "A Fitted Linear Multistep Approach for Singularly Perturbed Parabolic-Type Reaction–Diffusion Problems Using Shishkin Meshes," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2025, pages 1-16, September.
    11. Tesfaye Aga Bullo & Firdous A. Shah, 2022. "Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, March.
    12. Amare Worku Demsie & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "A Uniformly Convergent Scheme for Singularly Perturbed Unsteady Reaction–Diffusion Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    13. Bellen, Alfredo & Zennaro, Marino, 2013. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780199671373.
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