CAS小波求高阶Volterra积分微分方程数值解

CAS wavelets method for solving higher order Volterra integro-differential equations

考虑求高阶Volterra积分微分方程的数值解.利用小波的正交性质及矩阵的稀疏性,给出了CAS小波的积分算子矩阵;利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,简化了计算空间;最后,通过数值算例证明了该方法的有效性,并且得到更高精度的数值解.

In this paper,a kind of higher order Volterra integro-differential equation is discussed by using the property of wavelet and the sparse of matrix.The operational matrix of CAS wavelet is given.And then,the CAS wavelet operational matrix is utilized to reduce the higher order integro-differential equation to the algebraic equations and computation became convenient.Some illustrative examples are included to demonstrate the validity and the precision of the approach,and the precision of the obtained numerical solutions are higher.