Discretization principles for linear two-point boundary value problems, III

Tetsuro Yamamoto; Shin'Ichi Oishi; M. Zuhair Nashed; Zi Cai Li; Qing Fang

doi:10.1080/01630560802418367

Discretization principles for linear two-point boundary value problems, III

Tetsuro Yamamoto^*, Shin'Ichi Oishi, M. Zuhair Nashed, Zi Cai Li, Qing Fang

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29:213-224) to the boundary value problem [image omitted] where the sign of r(x) is indefinite. Let H_νA_νU^ν= f^ν be the finite difference equations on partitions [image omitted], =1,2, with [image omitted] as , where H_ν and A _ν are diagonal and tridiagonal matrices, respectively, and f ^ν are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u ∈ C²[a, b] are given in terms of [image omitted] and [image omitted].

Original language	English
Pages (from-to)	1180-1200
Number of pages	21
Journal	Numerical Functional Analysis and Optimization
Volume	29
Issue number	9-10
DOIs	https://doi.org/10.1080/01630560802418367
Publication status	Published - 2008 Sept

Keywords

Discretization principles
Finite difference methods
Two-point boundary value problems

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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10.1080/01630560802418367

Cite this

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abstract = "This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29:213-224) to the boundary value problem [image omitted] where the sign of r(x) is indefinite. Let HνAνUν= fν be the finite difference equations on partitions [image omitted], =1,2, with [image omitted] as , where Hν and A ν are diagonal and tridiagonal matrices, respectively, and f ν are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u ∈ C2[a, b] are given in terms of [image omitted] and [image omitted].",

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T1 - Discretization principles for linear two-point boundary value problems, III

AU - Yamamoto, Tetsuro

AU - Oishi, Shin'Ichi

AU - Nashed, M. Zuhair

AU - Li, Zi Cai

AU - Fang, Qing

PY - 2008/9

Y1 - 2008/9

N2 - This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29:213-224) to the boundary value problem [image omitted] where the sign of r(x) is indefinite. Let HνAνUν= fν be the finite difference equations on partitions [image omitted], =1,2, with [image omitted] as , where Hν and A ν are diagonal and tridiagonal matrices, respectively, and f ν are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u ∈ C2[a, b] are given in terms of [image omitted] and [image omitted].

AB - This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29:213-224) to the boundary value problem [image omitted] where the sign of r(x) is indefinite. Let HνAνUν= fν be the finite difference equations on partitions [image omitted], =1,2, with [image omitted] as , where Hν and A ν are diagonal and tridiagonal matrices, respectively, and f ν are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u ∈ C2[a, b] are given in terms of [image omitted] and [image omitted].

KW - Discretization principles

KW - Finite difference methods

KW - Two-point boundary value problems

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Discretization principles for linear two-point boundary value problems, III

Abstract

Keywords

ASJC Scopus subject areas

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