Applying topological method,this paper investigates the existence of positive solu-tions to singular m-point boundary value problems of a coupled system of differential equations.
Several existence results of solutions of two-point boundary value problems of Duffing type systems with Dirichlet boundary conditions, Neumann boundary conditions and periodic boundary conditions are presented.
Acceptable glycemic control when examining the effects of meals was </span></span><span><span><span style="font-family:"">achieved when combining basal insulin therapy and ...Acceptable glycemic control when examining the effects of meals was </span></span><span><span><span style="font-family:"">achieved when combining basal insulin therapy and high concentration insulin injection before a meal, when using a PID controller (Proportionality, Integrity and Derivative actions) alone, when using a PID controller with basal insulin therapy and when combining the three methods of insulin delivery. Naturally, a type 1 diabetic must inject himself with insulin in well-measured doses. Thus, the management and control of diabetes become a complex task when one must be considered the disturbance due to nutrition and sports activity. This concern has been at the center of much research through different approaches through mathematical methods and Artificial Intelligence methods. This article simulates a physiological model of glycemic control in type 1 diabetics by a PID regulatory mechanism, in the context of disturbances caused by the patient’s meals and athletic activity.展开更多
The HIV infection model of CD4＋ T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein poly...The HIV infection model of CD4＋ T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials （OBPs）. By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton＇s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.展开更多
In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4...In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4） （2016） 989-1020] to the problem of prostate cancer immunotherapy. We extend this method in two directions： first, we apply the method to a system of nonlinear ordinary differential equation, and second, we propose a new technique for finding the base functions in the considered algorithm.展开更多
基金Supported by the National Natural Science Foundation of China (10671167).
文摘Applying topological method,this paper investigates the existence of positive solu-tions to singular m-point boundary value problems of a coupled system of differential equations.
文摘Several existence results of solutions of two-point boundary value problems of Duffing type systems with Dirichlet boundary conditions, Neumann boundary conditions and periodic boundary conditions are presented.
文摘Acceptable glycemic control when examining the effects of meals was </span></span><span><span><span style="font-family:"">achieved when combining basal insulin therapy and high concentration insulin injection before a meal, when using a PID controller (Proportionality, Integrity and Derivative actions) alone, when using a PID controller with basal insulin therapy and when combining the three methods of insulin delivery. Naturally, a type 1 diabetic must inject himself with insulin in well-measured doses. Thus, the management and control of diabetes become a complex task when one must be considered the disturbance due to nutrition and sports activity. This concern has been at the center of much research through different approaches through mathematical methods and Artificial Intelligence methods. This article simulates a physiological model of glycemic control in type 1 diabetics by a PID regulatory mechanism, in the context of disturbances caused by the patient’s meals and athletic activity.
文摘The HIV infection model of CD4＋ T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials （OBPs）. By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton＇s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.
文摘In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4） （2016） 989-1020] to the problem of prostate cancer immunotherapy. We extend this method in two directions： first, we apply the method to a system of nonlinear ordinary differential equation, and second, we propose a new technique for finding the base functions in the considered algorithm.
