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Uniformly Convergent Scheme for Singularly Perturbed Space Delay Parabolic Differential Equation with Discontinuous Convection Coefficient and Source Term

Author

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  • Mulunesh Amsalu Ayele
  • Awoke Andargie Tiruneh
  • Getachew Adamu Derese

Abstract

A singularly perturbed delay parabolic problem of convection‐diffusion type with a discontinuous convection coefficient and source term is examined. In the problem, strong interior layers and weak boundary layers are exhibited due to a large delay in the spatial variable and discontinuity of convection coefficient and source. The problem is discretized by a nonstandard finite difference scheme in the spatial variable and for the time derivative, we used the Crank–Nicolson scheme. To enhance the order of convergence of the spatial variable, the Richardson extrapolation technique is applied. The error analysis of the proposed scheme was carried out and proved that the scheme is uniformly convergent of second order in both spatial and temporal variables. Numerical experiments are performed to verify the theoretical estimates.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1874741
    DOI: 10.1155/2022/1874741
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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. Wakjira Tolassa Gobena & Gemechis File Duressa, 2021. "Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-16, December.
    3. 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).
    4. Singh, Maneesh Kumar & Natesan, Srinivasan, 2018. "Richardson extrapolation technique for singularly perturbed system of parabolic partial differential equations with exponential boundary layers," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 254-275.
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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. 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).
    3. Yimesgen Mehari Kebede & Awoke Andargie Tiruneh & Endalew Getnet Tsega, 2025. "Hybrid Fitted Mesh Strategy for Singularly Perturbed Time‐Dependent Convection‐Diffusion Problems Featuring Boundary Turning Points," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).

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