Stability analysis of Jacobian-free iterative methods for solving nonlinear systems by using families of mth power divided differences

被引：0
|
作者：
A. R. Amiri
Alicia Cordero
M. T. Darvishi
Juan R. Torregrosa
机构：
[1] Razi University,Department of Mathematics, Faculty of Science
[2] Universitat Politècnica de València,Institute for Multidisciplinary Mathematics
来源：
Journal of Mathematical Chemistry | 2019年 / 57卷
关键词：
Nonlinear system of equations; Iterative method; Jacobian-free scheme; Divided difference; Basin of attraction; Order of convergence;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The dynamical properties of a family of forward, central divided differences and Richardson extrapolation technique are studied. Applying these tools, an iterative method for solving nonlinear systems can be transformed in a Jacobian-free scheme. We analyze the dynamical behavior of new schemes obtained in this way on low degree polynomial systems. Several chemical problems are solved by using these new techniques, confirming the theoretical results. In one of these problems (Chandrasekhar H-equation), a degenerated case with singular Jacobian is analyzed, obtaining good results.
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页码：1344 / 1373
页数：29
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