Fredholm积分微分方程的Haar小波数值解(英文)

Numerical solution of Fredholm integral-differential equations by using Haar wavelet

应用Haar小波求解Fredholm积分微分方程,引入了Haar小波、Haar小波积分算子矩阵,以此为基础建立了Fredholm积分微分方程的Haar小波数值方法.数值试验充分说明文中建议的方法的可行性、有效性和数值稳定性.这种方法的关键在于把原方程转化为代数方程,通过对代数方程求解,从而得到原方程的数值解,这样做的目的是为了降低求解问题的难度,使原来特别复杂和困难的问题转而容易解决.

Haar wavelet was used to solve Fredholm integral-differential equation. An operational matrix of integration based on Haar wavelets was introduced, and aprocedure for applying this matrix to solve Fredholm integral-differential equations with boundary conditions was formulated. The efficiency of the proposed method is tested with the aid of examples.