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

Bakytzhan Kurmanbek, Yogi A. Erlangga, Yerlan Amanbek

Results in Applied Mathematics, 2021

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DOI 10.1016/j.rinam.2021.100164

Data confidence 70 medium

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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.