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Article · Results in Applied Mathematics · June 18, 2021
Explicit inverse of near Toeplitz pentadiagonal matrices related to higher order difference operators
Bakytzhan Kurmanbek, Yogi A. Erlangga, Yerlan Amanbek
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.
Matrix Theory and AlgorithmsDifferential Equations and Boundary ProblemsNonlinear Differential Equations Analysispentadiagonal matricesmatrix inversefinite difference discretization
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