• 论文 •

### 一种新的求非线性方程组的数值延拓法

1. 1. 四川师范大学数学与软件科学学院, 成都 610066;
2. 内江师范学院四川省高等学校数值仿真重点实验室, 内江 641112;
3. 重庆市巴川中学, 重庆 402569
• 收稿日期:2015-12-28 出版日期:2017-02-15 发布日期:2017-02-17
• 通讯作者: 吴开腾, E-mail:ktengwu@njtc.edu.cn.
• 基金资助:

国家自然科学基金青年基金（11502121），四川省教育厅创新团队计划项目（13TD00001）和内江师范学院重点学科“计算数学”（0430101）资助.

Guo Jun, Wu Kaiteng, Zhang Li, Xia Linlin. A NEW CLASS OF NUMERICAL CONTINUATION METHOD FOR SOLVING THE NONLINEAR EQUATIONS[J]. Mathematica Numerica Sinica, 2017, 39(1): 33-41.

### A NEW CLASS OF NUMERICAL CONTINUATION METHOD FOR SOLVING THE NONLINEAR EQUATIONS

Guo Jun1, Wu Kaiteng2, Zhang Li2, Xia Linlin3

1. 1. College of Mathematics and Soft Science, Sichuan Normal University, Chengdu 610066, China;
2. Key Laboratory of Numerical Simulation in Sichuan Province, Neijiang Normal University, Neijiang 641100, China;
3. The Bachuan Middle School, Chongqing 402569, China
• Received:2015-12-28 Online:2017-02-15 Published:2017-02-17

In order to solve the Jacobi singular problem in the process of the iteration,in this paper,a new numerical continuation method is proposed.The Jacobi singularity is overcome by constructing the double-parameter homotopy operator,using controlled conditions and selecting appropriate parameter,and the convergence of this method is analyzed.Finally,the feasibility and superiority of this method is validated by numerical comparison,especially with the advantages of crossing the Jacobi singular problem (points,lines,surfaces).Thus,to an extent,this method can also solve the problem of being heavily dependent on the initial value,which is the shortcoming of the numerical continuation method.

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