Finite-difference method for singular nonlinear systems

被引：2

作者：

Buhmiler, Sandra ^{[1
]}

Rapajic, Sanja ^{[2
]}

Medic, Slavica ^{[1
]}

Grbic, Tatjana ^{[1
]}

机构：

[1] Univ Novi Sad, Dept Fundamental Sci, Fac Tech Sci, Trg Dositeja Obradovica 6, Novi Sad 21000, Serbia

[2] Univ Novi Sad, Dept Math & Informat, Fac Sci, Trg Dositeja Obradovica 3, Novi Sad 21000, Serbia

来源：

NUMERICAL ALGORITHMS | 2018年 / 79卷 / 01期

关键词：

Singular nonlinear system; Bordered system; Rank deficiency; Finite-difference approximation; NEWTONS METHOD; EQUATIONS; COMPUTATION; POINTS;

D O I：

10.1007/s11075-017-0428-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a method for solving nonlinear system with singular Jacobian at the solution. The convergence rate in the case of singularity deteriorates and one way to accelerate convergence is to form bordered system. A local algorithm, with finite-difference approximations, for forming and solving such system is proposed in this paper. To overcome the need that initial approximation has to be very close to the solution, we also propose a method which is a combination of descent method with finite-differences and local algorithm. Some numerical results obtained on relevant examples are presented.

引用

页码：65 / 86

页数：22

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