### 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_{ν}A_{ν}U^{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 ∈ C^{2}[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 | |

Publication status | Published - 2008 Sep |

### Fingerprint

### Keywords

- Discretization principles
- Finite difference methods
- Two-point boundary value problems

### ASJC Scopus subject areas

- Analysis
- Control and Optimization
- Signal Processing
- Computer Science Applications

### Cite this

*Numerical Functional Analysis and Optimization*,

*29*(9-10), 1180-1200. https://doi.org/10.1080/01630560802418367

**Discretization principles for linear two-point boundary value problems, III.** / Yamamoto, Tetsuro; Oishi, Shinichi; Nashed, M. Zuhair; Li, Zi Cai; Fang, Qing.

Research output: Contribution to journal › Article

*Numerical Functional Analysis and Optimization*, vol. 29, no. 9-10, pp. 1180-1200. https://doi.org/10.1080/01630560802418367

}

TY - JOUR

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

AU - Yamamoto, Tetsuro

AU - Oishi, Shinichi

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

UR - http://www.scopus.com/inward/record.url?scp=56349102291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56349102291&partnerID=8YFLogxK

U2 - 10.1080/01630560802418367

DO - 10.1080/01630560802418367

M3 - Article

VL - 29

SP - 1180

EP - 1200

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

SN - 0163-0563

IS - 9-10

ER -