基于最小二乘支持向量机的一维波动方程近似解求法  

Approximate Solutions to One Dimensional Wave Equation Based on Method of Least Squares Support Vector Machine

作　　者：程冰[1] 于加举[1] 吴自库[1] 陈秀荣[1] CHENG Bing;YU Jiaju;WU Ziku;CHEN Xiurong(School of Science and Information Science,Qingdao Agricultural University,Qingdao 266109,China)

机构地区：[1]青岛农业大学理学与信息科学学院,山东青岛266109

出　　处：《青岛农业大学学报（自然科学版）》2022年第3期230-234,共5页Journal of Qingdao Agricultural University(Natural Science)

基　　金：青岛农业大学教学研究项目(ZCJG202117;XJY2018022;XJY2019035);教育部产学合作协同育人项目(201902040018);青岛农业大学思政课题(XJY2021026)。

摘　　要：提出了一维波动方程的基于最小二乘支持向量机方法的近似解求法。该方法求得的近似解结构简单、精度高、形式固定。所得近似解由两部分组成:一部分是满足边值条件的已知函数;另一部分是两项的乘积,其中一项是边值为0的已知函数,另一项是与径向核函数相关的函数。同时证明了解的收敛性和稳定性,最后通过两个数值算例验证了该方法的有效性。An approximate solution method of the one-dimensional wave equation based on the method of least squares support vector machine is proposed.The approximate solution obtained by this method is simple in structure,high in precision and fixed in form.The obtained approximate solutions consist of two parts:One is a known function that satisfies the boundary value condition.The other is the product of two terms,one of which is a known function with zero boundary value,and the other is the function that is related to the radial kernel function.Meanwhile,the convergence and stability of the solution were proved,and the effectiveness of the method was verified by two numerical examples.

关 键 词：最小二乘支持向量机 波动方程 近似解 

分 类 号：O24[理学—计算数学]