A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots ...A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.展开更多
Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonline...Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonlinear excitations such as the algebraic lump-type line solitons, the lumpoff-type half line solitons, and segment solitons.展开更多
基金Foundation item： Supported by the National Science Foundation of China（10701066） Supported by the National Foundation of the Education Department of Henan Province（2008A110022）
文摘A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.
基金Supported by National Natural Science Foundation of China under Grant No.11435005Ningbo Natural Science Foundation(No.2015A610159)+1 种基金granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502sponsored by K.C.Wong Magna Fund in Ningbo University
文摘Jimbo-Miwa(JM) equation is one of the famous(3+1)-dimensional conditionally integrable nonlinear dynamical systems. It is pointed out that JM equation and its generalized form possess some types of interesting nonlinear excitations such as the algebraic lump-type line solitons, the lumpoff-type half line solitons, and segment solitons.
