A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models
No Thumbnail Available
Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
A novel matrix method based on the Taylor series called Taylor-Splitting Collocation Method is presented to solve linear and nonlinear ordinary differential equations. Unlike the previous approaches, the fundamental matrix equation is reformulated using interval splitting. The residual error estimation algorithm is presented. Convergence analysis is given in a general form. Four different mechanical models are analyzed: 1. Forced oscillations of a linear spring-mass model 2. Forced oscillations of a nonlinear spring-mass model 3. Free oscillations of a cubic nonlinear spring-dashpot-mass model 4. Forced oscillations of a damped nonlinear pendulum model Displacement-time and velocity-time dependencies are plotted for each model. Phase portraits of nonlinear models are presented. Appropriate absolute or residual error analyses are obtained for the proposed application models. The results of the new solution approach are compared with exact, numerical, and approximate solutions from previous works. Consistent results are found. © 2022 Elsevier Ltd
Description
Keywords
Matrix algebra , Nonlinear equations , Ordinary differential equations , Collocation approaches , Collocation method , Engineering modelling , Forced oscillations , Interval splitting , matrix , Matrix collocation method , Nonlinear oscillation , Splittings , Taylor polynomials , Vibrations (mechanical)