Document Type
Article
Source of Publication
Results in Applied Mathematics
Publication Date
8-1-2021
Abstract
This paper analyzes the inverse of near Toeplitz pentadiagonal matrices, arising from a finite-difference approximation to the fourth-order nonlinear beam equation. Explicit non-recursive inverse matrix formulas and bounds of norms of the inverse matrix are derived for the clamped–free and clamped–clamped boundary conditions. The bound of norms is then used to construct a convergence bound for the fixed-point iteration of the form u=f(u) for solving the nonlinear equation. Numerical computations presented in this paper confirm the theoretical results.
DOI Link
ISSN
Publisher
Elsevier
Volume
11
Disciplines
Physical Sciences and Mathematics
Keywords
Explicit formula, Finite difference, Fixed point method, Near Toeplitz, Nonlinear beam equation, Pentadiagonal matrices
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Kurmanbek, Bakytzhan; Erlangga, Yogi; and Amanbek, Yerlan, "Explicit inverse of near Toeplitz pentadiagonal matrices related to higher order difference operators" (2021). All Works. 4354.
https://zuscholars.zu.ac.ae/works/4354
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Hybrid: This publication is openly available in a subscription-based journal/series