A Programming Code for the Numerical Treatment of an Abstract Nonlinear System of Coupled Hyperbolic Equations Associated with the Timoshenko Model
Year: 2026
Type: software
Abstract: This source code corresponds to the combined numerical schemes developed to obtain numerical solutions of an abstract nonlinear system of coupled hyperbolic equations arising from the Timoshenko model. We propose a symmetric semi-discrete time-stepping scheme for this system, which reduces the original problem to a linear one and allows for parallel computation of its solution. Subsequently, a one-dimensional nonlinear dynamic Timoshenko beam system is considered, and the Legendre–Galerkin spectral method is employed for spatial discretization. Choosing differences of Legendre polynomials in the Galerkin method yields a sparse linear system that can be decoupled. The inner products used in the proposed algorithm are computed approximately using Gauss–Legendre quadrature.
Authors: Rogava, Jemal, Vashakidze, Zurab
Institutions: Tbilisi State University, University of Georgia
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7124708696