Highly Accurate Scheme for the Cauchy Problem of the Generalized Burgers-Huxley Equation

doi:10.12700/aph.13.6.2016.6.10

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Cited by 4 publications

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“…follows that ( ) j k t can be defined as continuous functions on ( ) 0, ∞ . Then, Equation (32) and inequality (33) imply that ( ),…”

Section: ( )mentioning

confidence: 99%

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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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“…follows that ( ) j k t can be defined as continuous functions on ( ) 0, ∞ . Then, Equation (32) and inequality (33) imply that ( ),…”

Section: ( )mentioning

confidence: 99%

“…In the same year, J. A. T. Machado et al introduced an algorithm, based on adopting the approximate analytical solution of the Cauchy problem for the Burgers-Huxley equation [33]. In 2017, B. Inan presented an explicit exponential finite difference method to solve the generalized forms of the Huxley and Burgers-Huxley equations [34].…”

Section: Introductionmentioning

confidence: 99%