The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . T...The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .展开更多
A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u' = nu, epsilon nu' + f(x, u, u')nu' - g(x, ...A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u' = nu, epsilon nu' + f(x, u, u')nu' - g(x, u, u') nu = 0 (0 < epsilon much less than 1). The asymptotic expansions of solutions are constructed, the remainders are estimated. The former works are improved and generalized.展开更多
In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells model.In this technique,the derivative in the nonlinear model is approximated by utilizing Haar funct...In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells model.In this technique,the derivative in the nonlinear model is approximated by utilizing Haar functions.The value of the unknown function is obtained by the process of integration.Error estimation is also discussed,which aims to reduce the error of numerical solutions.The numerical results show that the method is simply applicable.The results are compared with Runge-Kutta technique,Bessel collocation technique,LADM-Pade and Galerkin technique available in the literature.The results show that the Haar technique is easy,precise and effective.展开更多
Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equati...Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus （HIV） infection model of CD4^＋T cells and the susceptible-infected-removed （SIR） epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian （SBL） method. This method reduces the solution of such system to a system of linear or non- linear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge-Kutta （RK4） method and with the solutions obtained by some other methods in the literature.展开更多
文摘The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .
文摘A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u' = nu, epsilon nu' + f(x, u, u')nu' - g(x, u, u') nu = 0 (0 < epsilon much less than 1). The asymptotic expansions of solutions are constructed, the remainders are estimated. The former works are improved and generalized.
文摘In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells model.In this technique,the derivative in the nonlinear model is approximated by utilizing Haar functions.The value of the unknown function is obtained by the process of integration.Error estimation is also discussed,which aims to reduce the error of numerical solutions.The numerical results show that the method is simply applicable.The results are compared with Runge-Kutta technique,Bessel collocation technique,LADM-Pade and Galerkin technique available in the literature.The results show that the Haar technique is easy,precise and effective.
文摘Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus （HIV） infection model of CD4^＋T cells and the susceptible-infected-removed （SIR） epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian （SBL） method. This method reduces the solution of such system to a system of linear or non- linear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge-Kutta （RK4） method and with the solutions obtained by some other methods in the literature.
