High-Order Numerical Methods for Caputo Vibration Analysis in Automotive Engines

This paper presents a stable, high-order numerical method for solving Caputo differential equations that describe vibrational behavior in automotive engines. The proposed algorithm is based on a high-order fractional Runge-Kutta (FORK) method and is capable of identifying both Caputo parameters and the physical parameters of the system from simulation or experimental data with high accuracy. The efficient implementation in Python allows for simultaneous evaluation of accuracy, stability, and computational cost. Simulation results show that this method provides lower errors, higher stability, and more accurate parameter identification compared to classical methods. Furthermore, system response plots and parameter sensitivity analysis are provided, demonstrating the potential of this method in the development of advanced numerical methods in mechanical and automotive systems. The proposed framework is designed to be computationally efficient and suitable for engineering applications requiring long-term numerical integration of fractional-order dynamic systems. The combination of high-order discretization, predictor-corrector concepts, and parameter estimation improves the robustness of the numerical solution while preserving computational efficiency. These characteristics indicate that the proposed approach can serve as a practical numerical tool for future research on fractional vibration models, intelligent monitoring systems, and advanced simulation of complex engineering structures.

کلیدواژه ها:

automotive engine ، Caputo vibration ، high-order numerical method ، parameter identification ، Python simulation ، stable algorithm