Second-order robust finite difference method for singularly perturbed Burgers' equation

Kabeto, Masho Jima; Duressa, Gemechis File

doi:10.1016/j.heliyon.2022.e09579

Cited by 3 publications

(5 citation statements)

References 24 publications

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“…From the works in [2,3,4], for the parameter, , 1 ε = the solution for Eq. (2.2), is given by: ( , ) ( )exp( ).…”

Section: Formulation Of the Numerical Schemementioning

confidence: 99%

“…Following the works by Kabeto, and Duressa [2][3][4], to linearize Eq. (2.1), by applying the quasilinearization technique on the nonlinear term, for the reasonable initial guess of the form of Eq.…”

Section: Formulation Of the Numerical Schemementioning

confidence: 99%

“…In this section, we have chosen two model examples of singularly perturbed Burger-Huxley equations, since they have been widely discussed in the literature to validate our theoretical results. The maximum absolute errors are calculated by the double mesh principle [2][3][4], which is given by:…”

Section: Numerical Illustrationsmentioning

confidence: 99%

“…We need approximations since we either cannot solve analytically or the exact method is intractable. Hence, researchers are working on the solution methodologies of singularly perturbed Burger-Huxley equations, [4,5]. Thus, researchers tried to develop different methods to solve these equations that served as a ground to get prior knowledge and the limitations of the existing methods.…”

Section: Introductionmentioning

confidence: 99%

“…Further, the concerned researcher can find a real-time application of the modeled problem of Eq. (1.1) and its analytical properties such as the existence, stability, and boundness of the solutions in the literature [1][2][3][4][5][6]…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Accurate Computational Approach for Singularly Perturbed Burger-Huxley Equations

Bullo,

Kabeto,

Debela

et al. 2024

International Journal of Applied Mechanics and Engineering

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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.

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“…From the works in [2,3,4], for the parameter, , 1 ε = the solution for Eq. (2.2), is given by: ( , ) ( )exp( ).…”

Section: Formulation Of the Numerical Schemementioning

confidence: 99%

Section: Formulation Of the Numerical Schemementioning

confidence: 99%