摘要
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.
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.
出处
《郑州大学学报（理学版）》
CAS
北大核心
2017年第1期17-23,共7页
Journal of Zhengzhou University:Natural Science Edition
基金
国家自然科学基金项目(11261041
11261045)
关键词
重心插值配点法
高精度
分数阶积分方程
无网格
barycentric interpolation collocation method
high precision
fractional order integral equation
mesh free
作者简介
虎晓燕（1989-），女，宁夏固原人，硕士研究生，主要从事积分方程数值解的研究，E—mail：huxiaoyancai@163．com；
通讯作者：韩惠丽（1972-），女，宁夏银川人，教授，主要从事积分方程数值解的研究，E-mail：nxhan@126.com．
