Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5143549 | Journal of Taibah University for Science | 2017 | 16 Pages |
Abstract
In this paper, the sixth-order compact finite difference method is presented for solving singularly perturbed 1D reaction-diffusion problems. The derivative of the given differential equation is replaced by finite difference approximations. Then, the given difference equation is transformed to linear systems of algebraic equations in the form of a three-term recurrence relation, which can easily be solved using a discrete invariant imbedding algorithm. To validate the applicability of the proposed method, some model examples have been solved for different values of the perturbation parameter and mesh size. Both the theoretical error bounds and the numerical rate of convergence have been established for the method. The numerical results presented in the tables and graphs show that the present method approximates the exact solution very well.
Related Topics
Physical Sciences and Engineering
Chemistry
Chemistry (General)
Authors
Fasika Wondimu Gelu, Gemechis File Duressa, Tesfaye Aga Bullo,