Legendre小波函数求解非线性Volterra积分微分方程组的数值解

Legendre Wavelet Method for Numerically Solving Nonlinear System of Volterra Integro-Differential Equations

Legendre小波函数被用于逼近非线性Volterra积分微分方程组的解,方法是基于Legendre小波的性质构建相应的积分算子矩阵,进而将原问题转化为关于未知解系数的线性方程组,通过求解该方程组,即得原问题的数值解.数值结果表明所述方法对于求解此类问题是行之有效的.

In this paper,Legendre wavelet method is applied to approximate the solutions of nonlinear system of Volterra integro-differential equations.Then the original problem is reduced to a system of linear algebraic equations regarding the unknown coefficients,the unknown solutions are obtained by solving the system.Lastly the obtained numerical results show that our method is effective and feasible.