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 e...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<sup>2</sup> [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.展开更多
<span style="font-family:Verdana;">In the present paper, we introduce a non-polynomial quadratic spline method for solving </span><span style="font-family:Verdana;"><span style...<span style="font-family:Verdana;">In the present paper, we introduce a non-polynomial quadratic spline method for solving </span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> boundary value problems. </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Third-order</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor </span><span style="font-family:Verdana;">theory, Newtonian fluid mechanics, optimal control, convection</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">diffusion</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> processes, hydrodynamics, aerodynamics, etc. These problems have various important applications in fluid dynamics. The procedure involves a reduction of a </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> partial differential equation to a first</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">order ordinary differential </span><span style="font-family:Verdana展开更多
文摘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<sup>2</sup> [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.
文摘<span style="font-family:Verdana;">In the present paper, we introduce a non-polynomial quadratic spline method for solving </span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> boundary value problems. </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Third-order</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;"> singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor </span><span style="font-family:Verdana;">theory, Newtonian fluid mechanics, optimal control, convection</span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">diffusion</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> processes, hydrodynamics, aerodynamics, etc. These problems have various important applications in fluid dynamics. The procedure involves a reduction of a </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">third-order</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> partial differential equation to a first</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">order ordinary differential </span><span style="font-family:Verdana
