使用直接离散化求解第一类Fredholm积分方程的误差估计

Error estimate on direct discretization of Fredholm integral equation of the first kind

讨论一类存在唯一解的第一类Fredholm积分方程的直接离散化方法:复化梯形方法,复化Simpson方法,以及高斯法。从理论上给出了使用不同离散化方法求解该类积分方程的误差估计,特别给出了方程右端项有扰动时的误差界。数值实验表明高斯法在一定条件下具有很好的效果。

Three direct discretization methods, including compound trapezoid method, compound Simpson method and Gauss method, are investigated for some Fredholm integral equation of the first kind, which has a unique solution. A theoretical analysis on error estimate is given on the direct discretization methods, especially on the case where there is a perturbation on the right-hand side. The numerical experiment indicates that Gauss method has a much better performance than the other two ones.