高阶积分微分方程小波数值解法

Wavelets numerical method for solving higher order integro-differential equations

为求高阶Volterra积分微分方程的数值解,提出CAS小波法.利用CAS小波的正交性质,及小波矩阵的稀疏性,同时给出了CAS小波的积分算子矩阵,运用小波算子矩阵将高阶积分微分方程化为线性代数方程组,简化计算,提出了CAS小波收敛性定理.结果表明:随着点数的增多,数值解的精度也越来越高.数值算例验证了理论的正确性和方法的有效性.

This paper considered a kind of higher order Volterra integro-differential equation by using CAS wavelet. Using the property of the CAS wavelet and the sparse of matrix, this study also provided the operational matrix of CAS wavelet. The CAS wavelet operational matrix was then utilized to reduce the higher order integro-differential equation to the algebraic equations and computation became convenient. The convergence of CAS wavelet was presented. The results show that the more points, the higher the precision of the numerieal solution. Finally, numerical examples were included to demonstrate the correctness Of the theory and validity of the approach.