An efficient computational technique for solving a fractional-order model describing dynamics of neutron flux in a nuclear reactor

Roul, Pradip; Rohil, Vikas; Espinosa-Paredes, Gilberto; Obaidurrahman, K.

doi:10.1016/j.anucene.2023.109733

Cited by 7 publications

(1 citation statement)

References 32 publications

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“…In 2020, Singh et al [28] employed the fourth-order collocation method to get numerical solutions of the Burgers-Fisher equation. Roul et al used B-spline collocation methods in various studies [29][30][31][32][33][34] to fnd solution of some important problems occurring in the feld of science and engineering. Recently, Kumar et al [35] used a spline approximation technique to solve the boundary value inverse problem associated with the generalized Burgers-Fisher and generalized Burgers-Huxley equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Burgers–Huxley Equation Using a Higher Order Collocation Method

Singh,

Dahiya,

Emadifar

et al. 2024

Journal of Mathematics

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In this paper, the collocation method with cubic B-spline as basis function has been successfully applied to numerically solve the Burgers–Huxley equation. This equation illustrates a model for describing the interaction between reaction mechanisms, convection effects, and diffusion transport. Quasi-linearization has been employed to deal with the nonlinearity of equations. The Crank–Nicolson implicit scheme is used for discretization of the equation and the resulting system turned out to be semi-implicit. The stability of the method is discussed using Fourier series analysis (von Neumann method), and it has been concluded that the method is unconditionally stable. Various numerical experiments have been performed to demonstrate the authenticity of the scheme. We have found that the computed numerical solutions are in good agreement with the exact solutions and are competent with those available in the literature. Accuracy and minimal computational efforts are the key features of the proposed method.

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