In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending ...In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending on the number of subintervals ＂n＂ are calculated by using Maple 18 and presented. These results are demonstrated graphically in a particular numerical example. An algorithm of this application is given by using Maple 18.展开更多
For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a pa...For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin.展开更多
文摘In this paper, the approximate solution to the linear fredholm-stieltjes integral equations of the second kind （LFSIESK） by using the generalized midpoint rule （GMR） is introduced. A comparison resu｜ts depending on the number of subintervals ＂n＂ are calculated by using Maple 18 and presented. These results are demonstrated graphically in a particular numerical example. An algorithm of this application is given by using Maple 18.
基金supported by the National Natural Science Foundation of China(No.11401285)the Foundation for Research in Experimental Techniques of Liaocheng University(No.LDSY2014110)
文摘For a class of cubic systems, the authors give a representation of the n th order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin.
