非线性变系数Bagley-Torvik方程的积分边值问题  

Integral Boundary Value Problems of the Nonlinear Bagley￣Torvik Equation

作　　者：刘雪铃 黄静 崔钰晗 LIU Xueling;HUANG Jing;CUI Yuhan(Department of Electronic and Information Engineering,Bozhou College,Bozhou 236800,China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800

出　　处：《洛阳理工学院学报（自然科学版）》2024年第1期82-86,96,共6页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

基　　金：安徽省教育厅自然科学研究重点项目(2022AH052415);安徽省教育厅自然科学基金项目(KJ2021A1150);亳州学院大学生创新项目(2022XJXM095);安徽省大学生创新创业项目(S202212926006)。

摘　　要：研究了一类非线性变系数Bagley-Torvik方程的积分边值问题。对非线性变系数Bagley-Torvik方程进行多次积分得到与之等价的Fredholm-Hammerstein积分方程,利用分段泰勒级数得到Fredholm-Hammerstein积分方程的数值解。通过例题验证了此方法的可行性与有效性,并给相应的误差估计。The integral boundary value problem of nonlinear with variable coefficients is studied.The Fredholm-Hammerstein integral equation is obtained from multiple integration of Bagley-Torvik equation.A new numerical method was used to construct an approximate solution of the Fredholm-Hammerstein integral equation.The feasibility and effectiveness of this method were verified through examples,and corresponding error estimates were provided.

关 键 词：非线性变系数Bagley-Torvik方程 积分边值 Fredholm-Hammerstein积分方程 数值解 积分法 

分 类 号：O241.4[理学—计算数学]