2021/04/06 by Bakytzhan Kurmanbek, Kurmanbek, Bakytzhan, Yogi A. Erlangga +3
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2104.02280
openalex publication_date 2021/04/06 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28
This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the properties of the inverse of the related pentadiagonal matrices, associated with the fourth-order nonlinear beam equation. This nonlinear problem is discretized using the finite difference method with the clamped-free and clamped-clamped boundary conditions in the one dimension. Explicit formulas for the inverse of the matrices and norms of the inverse are derived. In iterative process, the direct computation of inverse matrix allows to achieve an efficiency. Numerical results were provided.