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

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dc.contributor.authorÇayan S.
dc.contributor.authorÖzhan B.B.
dc.contributor.authorSezer M.
dc.date.accessioned2024-07-22T08:03:56Z
dc.date.available2024-07-22T08:03:56Z
dc.date.issued2022
dc.description.abstractA 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
dc.identifier.DOI-ID10.1016/j.chaos.2022.112683
dc.identifier.issn09600779
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/12485
dc.language.isoEnglish
dc.publisherElsevier Ltd
dc.subjectMatrix algebra
dc.subjectNonlinear equations
dc.subjectOrdinary differential equations
dc.subjectCollocation approaches
dc.subjectCollocation method
dc.subjectEngineering modelling
dc.subjectForced oscillations
dc.subjectInterval splitting
dc.subjectmatrix
dc.subjectMatrix collocation method
dc.subjectNonlinear oscillation
dc.subjectSplittings
dc.subjectTaylor polynomials
dc.subjectVibrations (mechanical)
dc.titleA Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models
dc.typeArticle

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