In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in ...In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.展开更多
The filled function algorithm is an important method to solve global optimization problems.In this paper,a parameter-free filled function is proposed for solving general global optimization problem,discuss the theoret...The filled function algorithm is an important method to solve global optimization problems.In this paper,a parameter-free filled function is proposed for solving general global optimization problem,discuss the theoretical properties of this function and give the corresponding algorithm.The numerical experiments on some typical test problems using the algorithm and the numerical results show that the algorithm is effective.Applying the filled function method to the parameter solving problem in the logical population growth model,and then can be effectively applied to Chinese population prediction.The experimental results show that the algorithm has good practicability in practical application.展开更多
文摘In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.
基金Supported by National Natural Science Foundation of China(Grant No.12071112,11471102)Basic Research Projects for Key Scientic Research Projects in Henan Province(Grant No.20ZX001).
文摘The filled function algorithm is an important method to solve global optimization problems.In this paper,a parameter-free filled function is proposed for solving general global optimization problem,discuss the theoretical properties of this function and give the corresponding algorithm.The numerical experiments on some typical test problems using the algorithm and the numerical results show that the algorithm is effective.Applying the filled function method to the parameter solving problem in the logical population growth model,and then can be effectively applied to Chinese population prediction.The experimental results show that the algorithm has good practicability in practical application.
