A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

被引：7

作者：

Watanabe, Yoshitaka ^{[1
,2
]}

Nakao, Mitsuhiro T. ^{[3
]}

机构：

[1] Kyushu Univ, Res Inst Informat Technol, Higashi Ku, 6-10-1 Hakozaki, Fukuoka 8128518, Japan

[2] Japan Sci & Technol Agcy, CREST, Tokyo, Japan

[3] Sasebo Coll, Natl Inst Technol, 1-1 Okishin Cho, Nagasaki 8571193, Japan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 276卷

关键词：

Functional equation; Differential equation; Residual form; Newton-like iteration; FINITE-ELEMENT SOLUTION; ELLIPTIC PROBLEMS; EXISTENCE; BOUNDS; CONSTANT;

D O I：

10.1016/j.amc.2015.12.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：239 / 251

页数：13

共 30 条

[1]

CIARLET P. G., 2002, Classics in Appl. Math., V40

[2]

Grisvard P, 2011, CLASS APPL MATH, V69, P1, DOI 10.1137/1.9781611972030

[3] Determination of the Babuska-Aziz constant for the linear triangular finite element [J].

Kikuchi, F ;

Liu, XF .

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2006, 23 (01) :75-82

[4] On the L2 a Priori Error Estimates to the Finite Element Solution of Elliptic Problems with Singular Adjoint Operator [J].

Kinoshita, T. ;

Hashimoto, K. ;

Nakao, M. T. .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2009, 30 (3-4) :289-305

[5] ON THE EXISTENCE OF POSITIVE SOLUTIONS OF SEMI-LINEAR ELLIPTIC-EQUATIONS [J].

LIONS, PL .

SIAM REVIEW, 1982, 24 (04) :441-467

[6] Some remarks on the behaviour of the finite element solution in nonsmooth domains [J].

Nakao, Mitsuhiro T. ;

Kinoshita, Takehiko .

APPLIED MATHEMATICS LETTERS, 2008, 21 (12) :1310-1314

[7] Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications [J].

Nakao, Mitsuhiro T. ;

Hashimoto, Kouji .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 218 (01) :106-115

[8] Numerical verification methods for solutions of semilinear elliptic boundary value problems [J].

Nakao, Mitsuhiro T. ;

Watanabe, Yoshitaka .

IEICE NONLINEAR THEORY AND ITS APPLICATIONS, 2011, 2 (01) :2-31

[9] A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems [J].

Nakao, MT ;

Hashimoto, K ;

Watanabe, Y .

COMPUTING, 2005, 75 (01) :1-14

[10] Numerical verification of solutions for nonlinear elliptic problems using an L∞ residual method [J].

Nakao, MT ;

Yamamoto, N .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 217 (01) :246-262

← 1 2 3 →