Parameter-uniform spline in compression method for singularly perturbed parabolic boundary turning point problem

Jian, Ding; Melesse, Wondwosen Gebeyaw; Gelu, Fasika Wondimu; Bedaso, Jemal Abdule

doi:10.22124/jmm.2026.33001.3005

Parameter-uniform spline in compression method for singularly perturbed parabolic boundary turning point problem

Articles in Press

Document Type : Research Article

Authors

¹ School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044 Jingsu, China

² Department of Mathematics, Dilla University, Dilla, 419 Southern State, Ethiopia

³ Department of Mathematics, Dilla University, Dilla, Ethiopia

10.22124/jmm.2026.33001.3005

Abstract

This study investigates a parameter-uniform numerical method for solving singularly perturbed parabolic boundary turning point problem. The continuous problem is discretized using a spline in compression method for the space derivative on a Shishkin mesh and the Crank-Nicolson method for the time derivative on an equidistant mesh. The error analysis shows that the method is parameter-uniformly convergent with an error bound of order $O(N_x^{-2}\ln^2 N_x+N_t^2)$, where $N_x$ is the numebr of space mesh intervals and $N_t$ is the number of time mesh intervals. Three test examples are used to perform several numerical experiments, and comparative analyses are presented to validate the applicability and efficiency of the proposed method.

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