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

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.