Robust numerical approach for singularly perturbed parabolic problems with discontinuous convection coefficients and source terms

Cheru, Shegaye Lema; Duressa, Gemechis File; Mekonnen, Tariku Birabasa

doi:10.22034/cmde.2025.63426.2831

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	Robust numerical approach for singularly perturbed parabolic problems with discontinuous convection coefficients and source terms
Computational Methods for Differential Equations
مقاله 23، دوره 14، شماره 4، دی 2026، صفحه 1890-1911 اصل مقاله (1.45 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.63426.2831
نویسندگان
Shegaye Lema Cheru^* ¹؛ Gemechis File Duressa²؛ Tariku Birabasa Mekonnen¹
¹Department of Mathematics, Wollega University, Nekemte, Ethiopia.
²Department of Mathematics, Jimma University, Jimma, Ethiopia.
چکیده
This study explores the numerical method for 1 − D singularly perturbed parabolic problems, influenced by two distinct parameters affecting diffusion and convection. With discontinuous convection and source terms, the solutions exhibit boundary and interior layers due to the perturbations and discontinuities. The time variable is first discretized using the implicit Euler method on a uniform mesh, followed by spatial discretization of the semi discrete problems with a non polynomial cubic spline incorporating an exponential fitting factor. The method is shown to be first-order accurate and uniformly convergent. Its efficiency is demonstrated through four test cases, yielding more accurate results than those reported in existing methods.
کلیدواژه‌ها
Singularly perturbed problems؛ Discontinuous convection and source term؛ Implicit Euler Method؛ Non-polynomial cubic spline

مراجع
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Robust numerical approach for singularly perturbed parabolic problems with discontinuous convection coefficients and source terms