A modified ancient Babylonian algorithm for nonlinear oscillators - Xu, Kaipeng; Yang, Fang; Zhou, Xingwei (Advances in Differential Equations and Control Processes, 2026)
This paper focuses on the frequency-amplitude relationship of nonlinear oscillators and proposes an improved ancient Babylonian algorithm. This algorithm constructs a solution framework based on linear and nonlinear operators in a unique iterative form, and cleverly selects the initial guess value and determines the frequency equation. Through in-depth exploration of several representative nonlinear oscillator examples (covering different forms of nonlinear terms and parameter settings), it fully demonstrates its specific operation and effectiveness verification process in the solution process. The results show that this algorithm performs well in weakly nonlinear oscillator problems, and the obtained results are highly consistent with existing methods or exact solutions. Moreover, it is equivalent to He’s frequency formula under specific conditions, strongly supporting the effectiveness of the latter. At the same time, it clearly reveals the influence of the law of the nonlinear term coefficient and amplitude on the accuracy of the algorithm. However, in the case of strongly nonlinear systems, the algorithm has certain limitations. This study combines ancient numerical wisdom with modern nonlinear dynamics, providing a computationally simple and effective tool for oscillator engineering, while also indicating directions for improvement to enhance strong nonlinear performance.