带弱奇异核非线性积分微分方程的收敛性分析

J4 ›› 2012, Vol. 47 ›› Issue (8): 60-63.

带弱奇异核非线性积分微分方程的收敛性分析

吴志勤¹,石东伟²

1. 许昌学院数学与统计学院, 河南许昌 461000; 2. 河南科技学院数学系, 河南新乡 453003

收稿日期:2012-01-31 出版日期:2012-08-20 发布日期:2012-12-24
作者简介:吴志勤(1965- ), 女, 硕士, 副教授,主要从事有限元方法及应用研究.Email:wzq6698@126.com
基金资助:
国家自然科学基金资助项目(10671184; 10971203);高等学校博士学科点专项基金(20094101110006);国家自然科学基金数学天元基金(11026154)

Convergence analysis for nonlinear integro-differential equations with a weakly singular kernel

WU Zhi-qin¹, SHI Dong-wei²

1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
2. Department of Mathematics, Henan Insititute of Science and Technology, Xinxiang 453003, Henan, China

Received:2012-01-31 Online:2012-08-20 Published:2012-12-24

摘要/Abstract

摘要：

利用双线性元对一类带弱奇异核非线性积分微分方程进行了研究。利用单元已有的高精度分析结果、借助投影算子和平均值技巧, 在各向异性网格下得到了比以往文献高一阶的L²-模最优误差估计。

关键词: 积分微分方程; 弱奇异核; 各向异性; 双线性元; 最优误差估计

Abstract:

The bilinear finite element approximate for a class of nonlinear integrodifferential equations with weakly singular kernel is studied. The optimal error estimate which is one order higher approximate than the results of the previous literature in L²-norm is derived for anisotropy meshes based on the known high accuracy analysis results of this element, the projection operator and the average skills meanvalue.
i

Key words: ntegro-differential equations; weakly singular kernel; anisotropy; blinear element; optimal error estimate

吴志勤1,石东伟2. 带弱奇异核非线性积分微分方程的收敛性分析[J]. J4, 2012, 47(8): 60-63.

WU Zhi-qin1, SHI Dong-wei2. Convergence analysis for nonlinear integro-differential equations with a weakly singular kernel[J]. J4, 2012, 47(8): 60-63.

参考文献

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed