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第二类端点奇异Fredholm积分方程的分数阶退化核方法

本站小编 Free考研考试/2021-12-27

王同科, 樊梦
天津师范大学数学科学学院, 天津 300387
收稿日期:2017-08-26出版日期:2019-03-15发布日期:2019-02-18


基金资助:国家自然科学基金(11471166)资助项目;天津市高等学校创新团队培养计划(TD13-5078)资助项目;2017年天津师范大学****创新团队培育计划(135202TD1703)资助项目.


FRACTIONAL ORDER DEGENERATE KERNEL METHODS FOR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND WITH ENDPOINT SINGULARITIES

Wang Tongke, Fan Meng
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
Received:2017-08-26Online:2019-03-15Published:2019-02-18







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本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法,设计了两种计算格式,一是在全区间上使用分数阶Taylor展开式近似核函数,二是在包含奇点的小区间上采用分数阶插值,在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件,并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果,且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围.
MR(2010)主题分类:
65R20

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