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All Journal Mikailalsys Journal of Mathematics and Statistics
Jemilu, Shehu
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Engineering Mathematics Mechanical Engineering

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Development of a Predictor-Corrector Algorithm for the Numerical Solution of the Time-Fractional Vibration Equation Iyanda, Falade Kazeem; Dikko, Dauda Alani; Adefemi, Adeyemo Kolawole; Akeem, Adepoju Ajibola; Muhammad, Muhammad Yusuf; Jemilu, Shehu
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i1.7658

Abstract

This study employs a predictor–corrector approach to solve the time-fractional vibration equation governing the transverse deflection of a cable of length L fixed at both ends. The model incorporates the Riemann–Liouville time-fractional derivative to accurately represent memory effects and damping behavior characteristic of composite and viscoelastic materials. Spatial discretization is performed using a finite difference method, while the temporal fractional derivative is approximated through a carefully formulated predictor–corrector scheme. This technique effectively addresses the initial conditions and captures the nonlocal temporal dynamics introduced by the fractional derivative. Numerical experiments demonstrate that the proposed method is accurate, stable, and computationally efficient in simulating damped vibrations in elastic and composite cables. By offering a reliable numerical framework, the approach enables more precise analysis of vibrating systems with memory effects and material heterogeneity, thereby contributing to improved modeling and design in engineering applications involving time-dependent mechanical behavior.
Co-Authors Adefemi, Adeyemo Kolawole Akeem, Adepoju Ajibola Dikko, Dauda Alani Iyanda, Falade Kazeem Muhammad, Muhammad Yusuf