Title: The application of mathematical analysis in solving nonlinear phenomena in fluid mechanics

Authors: You Li; Gui Li; Xuan Leng

Addresses: College of Science, Hunan City University, Yiyang, 413000, China ' College of Civil Engineering, Hunan City University, Yiyang, 413000, China ' College of Science, Hunan City University, Yiyang, 413000, China

Abstract: In order to assist mathematical analysis in solving nonlinear problems, reduce the computational cost and accelerate the solution process, the study explores the common mathematical methods for nonlinear solution; followed by the introduction of an optimised arithmetic algorithm for improved precision. Experimental results showed the hybrid algorithm designed in the study achieves a recall of 0.893, corresponding to a precision of 0.9, and a ROC region of 0.913, which is better than other algorithms in the same experimental environment. The algorithm demonstrated fast convergence in loss curve, high computational efficiency, taking only 9.07 s. The average absolute value error converges to 0.07, and the root mean square error converges to 0.532. The method takes the optimal values of Generation Distance, Hyper volume, Spacing and Spread indexes in the process of solving nonlinear equations. This study effectively combines the mathematical analytical method and computer technology to provide a new idea and method for the mathematical analysis of nonlinear phenomena, which enriches the research content of nonlinear science.

Keywords: solitons; abnormal wave; nonlinear phenomena; arithmetic optimisation algorithm; nonlinear equation.

DOI: 10.1504/IJCSM.2025.149609

International Journal of Computing Science and Mathematics, 2025 Vol.22 No.1, pp.90 - 106

Received: 22 Feb 2024
Accepted: 21 May 2025
Published online: 07 Nov 2025 *

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