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

Çayan S., ÖZHAN B. B., Sezer M.

Chaos, Solitons and Fractals, cilt.164, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 164
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.chaos.2022.112683
  • Dergi Adı: Chaos, Solitons and Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Anahtar Kelimeler: Matrix collocation method, Interval splitting, Taylor polynomial, Nonlinear oscillations, Mechanical vibrations
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

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.