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Accurate computational approach for singularly perturbed Burger-Huxley equations

Bullo Tesfaye Aga, Kabeto Masho Jima, Debela Habtamu Garoma, Kusi Gemadi Roba, Robi Habtamu Garoma

International Journal of Applied Mechanics and Engineering

2024

Vol. 29, no. 2

16--25

The main purpose of this work is to present an accurate computational approach for solving the singularly perturbed Burger-Huxley equations. The quasilinearization technique linearizes the nonlinear term of the differential equation. The finite difference approximation is formulated to approximate the derivatives in the differential equations and then accelerate its rate of convergence to improve the accuracy of the solution. Numerical experiments were conducted to sustain the theoretical results and to show that the presented method produces a more correct solution than some surviving methods in the literature.

Robust numerical method for singularly perturbed differential equations with large delay

Abdulla Murad Ibrahim, Duressa Gemechis File, Debela Habtamu Garoma

Demonstratio Mathematica

2021

Vol. 54, nr 1

576--589

In this paper, a singularly perturbed differential equation with a large delay is considered. The considered problem contains a large delay parameter on the reaction term. The solution of the problem exhibits the interior layer due to the delay parameter and the strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using the fitted non-polynomial spline method. The stability and parameter uniform convergence of the proposed method is proved. To validate the applicability of the scheme, two model problems of the variable coefficient are considered for numerical experimentation.