Extending the applicability of Newton?s method for a class of boundary value problems using the shooting method

被引：5

作者：

Argyros, I. K. ^{[1
]}

Ceballos, J. ^{[2
]}

Gonzalez, D. ^{[2
]}

Gutierrez, J. M. ^{[3
]}

机构：

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] Univ Amer, Escuela Ciencias Fis & Matemat, Quito 170125, Ecuador

[3] Univ La Rioja, Dept Matemat & Computac, Logrono 26006, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 384卷

关键词：

Boundary value problem; Lipschitz condition; Newton's method; Shooting method;

D O I：

10.1016/j.amc.2020.125378

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use Newton's method to approximate locally unique solutions for a class of boundary value problems by applying the shooting method. The utilized operator is Fréchet-differentiable between Banach spaces. These conditions are more general than those that appear in previous works. In particular, we show that the old semilocal and local convergence criteria for Newton's method involving Banach space value operators can be replaced by weaker ones. Hence, extending the applicability of the method. Several numerical examples are developed to test the new convergence criteria and also compare them to the old ones. © 2020 Elsevier Inc.

引用

页数：11

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