A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models

Seda Çayan, B. Burak Özhan and Mehmet Sezer

Chaos, Solitons & Fractals, 2022, vol. 164, issue C

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 model2.Forced oscillations of a nonlinear spring-mass model3.Free oscillations of a cubic nonlinear spring-dashpot-mass model4.Forced oscillations of a damped nonlinear pendulum model

Keywords: Matrix collocation method; Interval splitting; Taylor polynomial; Nonlinear oscillations; Mechanical vibrations (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008621

DOI: 10.1016/j.chaos.2022.112683

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