梁振动方程数值解的移位Legendre小波配置法  

Numerical Solution for the Beam Vibration Equation Using Shifted Legendre Wavelets Collocation Method

作　　者：周凤英 谢宇 ZHOU Feng-ying;XIE Yu(School of Science, East China University of Technology, Nanchang 330013 , China)

机构地区：[1]东华理工大学理学院

出　　处：《东华理工大学学报（自然科学版）》2019年第2期195-200,共6页Journal of East China University of Technology(Natural Science)

基　　金：国家自然科学基金(11601076);江西省教育厅科学技术研究项目(GJJ170473)

摘　　要：建立了求解梁振动方程数值解的移位Legendre小波配置法。利用移位的Legendre多项式,推导出Riemann-Liouville意义下移位Legendre小波函数的一般分数阶积分公式。利用分数积分公式和二维移位Legendre小波配置法,将梁振动方程求解问题转化为代数方程组求解。数值算例表明该方法具有较高的精度。Collocation method based on Shifted Legendre wavelet for solving the numerical solution of beam vibration equation is presented. The fractional integral formula of a single shifted Legendre wavelet function is derived from the definition by means of the shifted Legendre polynomial. Beam vibration equation is converted to a system of algebraic equation by using two dimensional shifted Legendre wavelet collocation methods and fractional integral formula. Numerical example shows that the method has high accuracy.

关 键 词：梁振动方程 LEGENDRE小波 配置法 分数阶积分 

分 类 号：O241.5[理学—计算数学]