具有超收敛性的积分方程的快速泛函逼近方法

Superconvergence of Fast Multiscale Functional Approximation for Integral Equations

主要构造第二类Fredholm积分方程的线性泛函解的具有超收敛性及高效率的快速泛函逼近框架,同时应用到小波Galerkin情形,构造快速多尺度Galerkin泛函逼近框架,并给出近似解的误差估计.

In this paper,we construct a fast functional approximation frame work for the linear functional of the solution of second kind Fredholm integral equations,and we provide the theory analysis for the approximation solution.In the end,we consider the wavelet Galerkin version,leading to the fast multiscale Galerkin functional approximation.We provide that under a suitable condition the framework exhibit super-convergence properties and high efficiency.