Nurullah Rasedee A.F.Ishak N.Hamzah S.R.Ijam H.M.Suleiman M.Ibrahim Z.B.Abdul Sathar M.H.Ramli N.A.Kamaruddin N.S.2024-05-282024-05-2820171742658810.1088/1742-6596/890/1/0120452-s2.0-85030662230https://www.scopus.com/inward/record.uri?eid=2-s2.0-85030662230&doi=10.1088%2f1742-6596%2f890%2f1%2f012045&partnerID=40&md5=0b5031e9bf027d6989bab12509e1e355https://oarep.usim.edu.my/handle/123456789/8805Nonlinear phenomena in science and engineering such as a periodically forced oscillator with nonlinear elasticity are often modeled by the Duffing oscillator (Duffing equation). The Duffling oscillator is a type of nonlinear higher order differential equation. In this research, a numerical approximation for solving the Duffing oscillator directly is introduced using a variable order stepsize (VOS) algorithm coupled with a backward difference formulation. By selecting the appropriate restrictions, the VOS algorithm provides a cost efficient computational code without affecting its accuracy. Numerical results have demonstrated the advantages of a variable order stepsize algorithm over conventional methods in terms of total steps and accuracy. � Published under licence by IOP Publishing Ltd.en-USArticle890112045