Accurate computational approach for singularly perturbed Burger-Huxley equations

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

Identyfikatory

DOI

10.59441/ijame/187049

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

singularly perturbed; nonlinear term; accurate solution

PL

równanie różniczkowe; różnice skończone; matematyka stosowana; równanie Burgera-Huxleya

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2024
• Tom: Vol. 29, no. 2
• Strony: 16--25
• Opis fizyczny: Bibliogr. 17 poz., wykr.

Twórcy

autor

Bullo Tesfaye Aga

• Mathematics, Jimma University, ETHIOPIA

• https://orcid.org/0000-0001-6766-4803

autor

Kabeto Masho Jima

• Mathematics, Jimma University, ETHIOPIA

autor

Debela Habtamu Garoma

• Mathematics, Jimma University, ETHIOPIA

autor

Kusi Gemadi Roba

• Mathematics, Jimma University, ETHIOPIA

autor

Robi Habtamu Garoma

• Mathematics, Jimma University, ETHIOPIA

Bibliografia

• [1] Li-Bin L., Ying L., Jian Z. and Xiaobing B. (2020): A robust adaptive grid method for singularly perturbed Burger- Huxley equations.– Electronic Research Archive, vol.28, No.4, pp.1439-1457.
• [2] Kabeto M.J. and Duressa G.F. (2021): Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations.– BMC Research Notes, vol.14, No.1, p.446.
• [3] Jima K.M. and File D.G. (2022): Implicit finite difference scheme for singularly perturbed Burger-Huxley equations.– J. Partial Differ. Equ., vol.35, No.1, pp.87-100.
• [4] Kabeto M.J. and Duressa G.F. (2022): Second-order robust finite difference method for singularly perturbed Burgers' equation.– Heliyon, vol.8, No.6.
• [5] Daba I.T. and Duressa G.F. (2022): A fitted numerical method for singularly perturbed Burger–Huxley equation.– Boundary Value Problems, vol.2022, No.1, p.102.
• [6] Kabeto M.J. and Duressa G.F. (2021): A robust numerical method for singularly perturbed semilinear parabolic differential-difference equations.– Mathematics and Computers in Simulation, vol.188, pp.537-547.
• [7] Bullo T.A. and Kusi G.R. (2023): Fitted mesh scheme for singularly perturbed parabolic convection–diffusion problem exhibiting twin boundary layers.– Reaction Kinetics, Mechanisms and Catalysis, pp.1-14.
• [8] Reda B.T., Bullo T.A. and Duressa G.F. (2023): Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems.– BMC Research Notes, vol.16, No.1, p.354.
• [9] Kusi G.R., Habte A.H. and Bullo T.A. (2023): Layer resolving numerical scheme for a singularly perturbed parabolic convection-diffusion problem with an interior layer.– MethodsX, vol.10, p.101953.
• [10] Woldaregay M.M., Hunde T.W. and Mishra V.N. (2023): Fitted exact difference method for solutions of a singularly perturbed time delay parabolic PDE.– Partial Differential Equations in Applied Mathematics, vol.8, p.100556.
• [11] Bullo T.A. (2022): Accelerated fitted mesh scheme for singularly perturbed turning point boundary value problems.– Journal of Mathematics, vol.2022, doi.org/10.1155/2022/3767246.
• [12] Bullo T.A., Degla G.A. and Duressa G.F. (2022): Fitted mesh method for singularly perturbed parabolic problems with an interior layer.– Mathematics and Computers in Simulation, vol.193, pp.371-384.
• [13] Bullo T.A., Duressa G.F. and Degla G. (2021): Accelerated fitted operator finite difference method for singularly perturbed parabolic reaction-diffusion problems.– Computational Methods for Differential Equations, vol.9, No.3, pp.886-898.
• [14] Bullo T.A., Degla G.A. and Duressa G.F. (2021): Uniformly convergent higher-order finite difference scheme for singularly perturbed parabolic problems with non-smooth data.– Journal of Applied Mathematics and Computational Mechanics, vol.20, No.1, pp.5-16.
• [15] Bullo T.A., Degla G.A. and Duressa G.F. (2022): Parameter-uniform finite difference method for a singularly perturbed parabolic problem with two small parameters.– International Journal for Computational Methods in Engineering Science and Mechanics, vol.23, No.3, pp.210-218.
• [16] Ejere A.H., Dinka T.G., Woldaregay M.M. and Duressa G.F. (2023): A tension spline fitted numerical scheme for singularly perturbed reaction-diffusion problem with negative shift.– BMC Research Notes, vol.16, No.1, pp.1-16.
• [17] Aniley W.T. and Duressa G.F. (2023): A uniformly convergent numerical method for time-fractional convection– diffusion equation with variable coefficients.– Partial Differential Equations in Applied Mathematics, vol.8, p.100592.