Bibliographic Details
| Title: |
Uniform numerical method for singularly perturbed parabolic time delay reaction-diffusion problems arising in control theory. |
| Authors: |
Huntul, Mousa J.1, Daba, Imiru Takele2 imirutakele@gmail.com |
| Source: |
Mathematical Modelling & Analysis. 2026, Vol. 31 Issue 3, p392-406. 15p. |
| Subjects: |
Singular perturbations, Reaction-diffusion equations, Finite difference method, Numerical analysis, Stability criterion, Crank-Nicolson method, Parabolic differential equations |
| Abstract: |
This paper introduces a uniform numerical scheme to find approximate solutions for singularly perturbed parabolic time delay reaction-diffusion problems. The scheme utilizes the Crank-Nicolson method for approximating time derivatives, combined with a novel finite difference method for spatial discretization. The stability and uniform convergence of the proposed scheme are investigated. The primary objective of this work is to demonstrate that the proposed scheme achieves a parameter-free error bound of order O(k2 + N-2). To validate the theoretical results, various numerical experiments have been conducted, showing that the proposed scheme yields superior results compared to some existing methods in the literature. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
