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A Fitted Linear Multistep Approach for Singularly Perturbed Parabolic‐Type Reaction–Diffusion Problems Using Shishkin Meshes

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

Abstract

This paper presents a class of singularly perturbed parabolic‐type reaction diffusion problems. Due to the presence of a small parameter ε, (0

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:5553428
    DOI: 10.1155/ijmm/5553428
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    References listed on IDEAS

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    1. 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).
    2. Mesfin Mekuria Woldaregay & Gemechis File Duressa & Nasser Hassen Sweilam, 2022. "Boundary Layer Resolving Exact Difference Scheme for Solving Singularly Perturbed Convection-Diffusion-Reaction Equation," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-16, December.
    3. Ababi Hailu Ejere & Gemechis File Duressa & Mesfin Mekuria Woldaregay & Tekle Gemechu Dinka & Birendra Nath Mandal, 2023. "A Parameter-Uniform Numerical Scheme for Solving Singularly Perturbed Parabolic Reaction-Diffusion Problems with Delay in the Spatial Variable," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2023, pages 1-17, March.
    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. Dagnachew Mengstie Tefera & Awoke Andargie Tiruneh & Getachew Adamu Derese, 2021. "Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    6. Sushree Priyadarshana & Jugal Mohapatra, 2024. "An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(4), pages 1389-1408, December.
    7. Kumar, Sunil & Sumit, & Ramos, Higinio, 2021. "Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    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. Dagnachew Mengstie Tefera & Awoke Andargie Tiruneh & Getachew Adamu Derese, 2021. "Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-12, October.
    10. Yimesgen Mehari Kebede & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "Fitted Operator Method for Singularly Perturbed Delay Parabolic Problems With Boundary Turning Points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2025, pages 1-15, February.
    11. Yimesgen Mehari Kebede & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "Fitted Operator Method for Singularly Perturbed Delay Parabolic Problems With Boundary Turning Points," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    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).
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    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).

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