The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. ...The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley equation. Also, the results prove that the method is an efficient and powerful algorithm to construct the exact solution of non-linear differential equations.展开更多
In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
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
By introducing and extending the G'/G expansion method with the aid of computer algebraic system “Mathematics”, the exact general solutions were obtained for the Burgers-Huxley equation and special form. Final r...By introducing and extending the G'/G expansion method with the aid of computer algebraic system “Mathematics”, the exact general solutions were obtained for the Burgers-Huxley equation and special form. Final results were represented in hyperbolic function, trigonometric function and rational function with arbitrary parameters.展开更多
In this paper,an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation.The quadratically convergent quasilinearization technique is used to linear...In this paper,an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation.The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation.The innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization technique.This basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under consideration.The derivatives are replaced by finite difference approximation,then we obtain the two-level time direction and the three-term recurrence relation in the spatial direction.The convergence analysis of the proposed method has been established.Numerical experiments were conducted to support the theoretical results.Further,the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.展开更多
文摘The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley equation. Also, the results prove that the method is an efficient and powerful algorithm to construct the exact solution of non-linear differential equations.
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
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By introducing and extending the G'/G expansion method with the aid of computer algebraic system “Mathematics”, the exact general solutions were obtained for the Burgers-Huxley equation and special form. Final results were represented in hyperbolic function, trigonometric function and rational function with arbitrary parameters.
文摘In this paper,an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation.The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation.The innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization technique.This basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under consideration.The derivatives are replaced by finite difference approximation,then we obtain the two-level time direction and the three-term recurrence relation in the spatial direction.The convergence analysis of the proposed method has been established.Numerical experiments were conducted to support the theoretical results.Further,the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.
