Accelerated Numerical Method for Singularly Perturbed Differential Difference Equations

Habtamu Garoma Debela, Gemechis File Duressa, Masho Jima Kebeto

Abstract


In this paper, accelerated finite difference method for solving singularly perturbed delay reaction-diffusion equations is presented. First, the solution domain is discretized. Then, the derivatives in the given boundary value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of equations is obtained, which can easily be solved by Thomas algorithm. The consistency, stability and convergence of the method have been established. To increase the accuracy of our established scheme we used Richardson's extrapolation techniques. To validate the applicability of the proposed method, four model examples have been considered and solved for different values of perturbation parameters and mesh sizes. The numerical results have been presented in tables and graphs to illustrate; the present method approximates the exact solution very well. Moreover, the present method gives better accuracy than the existing numerical methods mentioned in the literature.

Keywords


Singular perturbation; Delay differential equation; Fitted operator; Twin layers; Oscillatory layers

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DOI: http://dx.doi.org/10.12962/j24775401.v7i2.6859

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International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/ijcsam.