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

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

Document Type : Research Paper

Authors

¹ Department of Mathematics, Wollega University, Nekemte, Ethiopia.

² Department of Mathematics, Jimma University, Jimma, Ethiopia.

10.22034/cmde.2025.63426.2831

Abstract

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.

Keywords

Main Subjects

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

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