Exact solutions of the Burgers–Huxley equation via dynamics

Kushner, Alexei G.; Matviichuk, Ruslan I.

doi:10.1016/j.geomphys.2020.103615

Cited by 11 publications

(2 citation statements)

References 9 publications

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“…A. Kumar and M. T. Mohan introduced an analytical global solvability as well as asymptotic analysis of stochastic generalized Burgers-Huxley (SGBH) equation perturbed by space-time white noise in a bounded interval of R in 2020 [40]. A. G. Kushner (2020) constructed such dynamics for the classical Burgers-Huxley equation and then used them to construct new exact solutions [41]. More recently, L. Ebiwareme (2021) proposed the Tanh-coth and Banach contraction methods to solve the Burgers-Huxley and Kuramoto-Sivashinsky equations [42].…”

Section: Et Al Introduced a New Numerical Technique For Solving Nonli...mentioning

confidence: 99%

Adaptive Boundary Control for the Dynamics of the Generalized Burgers-Huxley Equation

Alaofi¹,

Ali²,

Alaal³

et al. 2022

OJAppS

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This paper deals with the boundary control problem of the unforced generalized Burgers-Huxley equation with high order nonlinearity when the spatial domain is [0, 1]. We show that this type of equations are globally exponential stable in L 2 [0, 1] under zero Dirichlet boundary conditions. We use an adaptive nonlinear boundary controller to show the convergence of the solution to the trivial solution and to show that it achieves global asymptotic stability in time. We introduce numerical simulation for the controlled equation using the Adomian decomposition method (ADM) in order to illustrate the performance of the controller.

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Section: Et Al Introduced a New Numerical Technique For Solving Nonli...mentioning

confidence: 99%

Adaptive Boundary Control for the Dynamics of the Generalized Burgers-Huxley Equation

Alaofi¹,

Ali²,

Alaal³

et al. 2022

OJAppS

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“…Recently, the exact solution has been computed by Kushner and Matviichuk [39] using the theory of finitedimensional dynamics. Shukla and Kumar [40] applied the numerical scheme based on the Crank-Nicolson finite difference method in collaboration with the Haar wavelet analysis, to obtain the numerical solution.…”

mentioning

confidence: 99%

Numerical Approximation of Generalized Burger’s-Fisher and Generalized Burger’s-Huxley Equation by Compact Finite Difference Method

Kaur

Shallu

Kumar

et al. 2021

Advances in Mathematical Physics

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In this work, computational analysis of generalized Burger’s-Fisher and generalized Burger’s-Huxley equation is carried out using the sixth-order compact finite difference method. This technique deals with the nonstandard discretization of the spatial derivatives and optimized time integration using the strong stability-preserving Runge-Kutta method. This scheme inculcates four stages and third-order accuracy in the time domain. The stability analysis is discussed using eigenvalues of the coefficient matrix. Several examples are discussed for their approximate solution, and comparisons are made to show the efficiency and accuracy of CFDM6 with the results available in the literature. It is found that the present method is easy to implement with less computational effort and is highly accurate also.

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Finite Dimensional Dynamics of Evolutionary Equations with Maple

Kushner

Matviichuk

2020

Differential Geometry, Differential Equations, and Mathematical Physics

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Exact solutions of the Burgers–Huxley equation via dynamics

Cited by 11 publications

References 9 publications

Adaptive Boundary Control for the Dynamics of the Generalized Burgers-Huxley Equation

Adaptive Boundary Control for the Dynamics of the Generalized Burgers-Huxley Equation

Numerical Approximation of Generalized Burger’s-Fisher and Generalized Burger’s-Huxley Equation by Compact Finite Difference Method

Finite Dimensional Dynamics of Evolutionary Equations with Maple

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