重心插值配点法求解分数阶Fredholm积分方程

摘要

Barycentric interpolation collocation method was the combination and promotion of interpolation method and the collocation method.It was a new kind of numerical calculation method which had excellent numerical stability, high precision,and computational efficiency.This new method was used to solve fractional order Fredholm integral equation, and was deduced discrete calculate formula of the barycentric interpolation collocation method of fractional order Fredholm integral equation.Through theoretical analysis, it derived its existence and uniqueness of solutions and error analysis.Finally,some numerical examples were used to contrast equidistant nodes and the second Chebyshev nodes to demonstrate the effectiveness and precision of this method, and then the conditions that affect the precision was obtained.%重心插值配点法是插值法和配点法的结合和推广,它具有稳定性好、高精度和计算效率高等优点.主要运用高精度无网格重心插值配点法求解分数阶Fredholm积分方程.首先推导了基于分数阶Fredholm积分方程重心插值配点法的离散公式,然后通过理论分析得出其解的存在唯一性与误差分析,最后利用数值算例通过对等距节点与第二类Chebyshev节点的对比,验证了所用方法的高精度和可靠性,并得出影响精度的条件.