应用数学和力学2026，Vol.47Issue(9)：1211-1221,11.DOI:10.21656/1000-0887.460144
应用Laplace变换和机器学习构造气泡方程的同伦分析解
Homotopy Analysis Solutions to Bubble Equations Through the Laplace Transform and Machine Learning
摘要
Abstract
The homotopy analysis method(HAM)is an important approach for solving nonlinear problems.The HAM was applied to construct high-precision approximate analytical solutions to the Rayleigh-Plesset equations for describing the periodic pulsation of bubbles in an ideal fluid.In the HAM framework,the Laplace transform was used to solve high-order deformation equations and obtain HAM solutions to the bubble equations.By means of the machine learning to optimize the convergence-control parameter in the HAM approximations,high-precision HAM approximations of the bubble equations were obtained.The results show that,the Laplace transform improves the efficiency of solving complex high-order deformation equations,and the machine learn-ing technique provides an effective way to optimize the convergence control parameter in HAM approximations.Finally,as applications of the HAM approximations,dynamic characteristics and laws of bubble pulsation were discussed.关键词
气泡方程/Laplace变换/机器学习/同伦分析方法/收敛控制参数Key words
bubble equation/Laplace transform/machine learning/homotopy analysis method/convergence-control parameter分类
数理科学引用本文复制引用
秦玉鹏,王烁,金昊,王振,邹丽..应用Laplace变换和机器学习构造气泡方程的同伦分析解[J].应用数学和力学,2026,47(9):1211-1221,11.基金项目
国家自然科学基金(12202139) （12202139）
中国博士后科学基金面上项目(2025M784397) （2025M784397）
河南省科技研发联合基金(235200810063) （235200810063）
河南省科技攻关项目(242102310429) （242102310429）
河南省自然科学基金(252300421803) （252300421803）
