Explicit inverse of near Toeplitz pentadiagonal matrices related to higher order difference operators

Bakytzhan Kurmanbek, Yogi Erlangga, Yerlan Amanbek

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number100164
JournalResults in Applied Mathematics
Volume11
DOIs
Publication statusPublished - Aug 2021

Keywords

  • Explicit formula
  • Finite difference
  • Fixed point method
  • Near Toeplitz
  • Nonlinear beam equation
  • Pentadiagonal matrices

ASJC Scopus subject areas

  • Applied Mathematics

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