数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 387-393.

• 论文 • 上一篇    下一篇

具有有界混合偏导核的积分方程自适应解的优化

段立芹   

  1. 杭州电子科技大学 数学研究所 杭州 310018
  • 收稿日期:2009-02-19 修回日期:2010-03-22 出版日期:2011-04-25 发布日期:2011-04-25
  • 基金资助:

    国家自然科学基金(10671019, 10926056)和杭州电子科技大学校科研启动基金(KYS091507089)资助

Optimization of Adaptive Direct Method for Approximate Solution of Integral Equations with Bounded Mixed Derivative Kernels

 DUAN Li-Qin   

  1. Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2009-02-19 Revised:2010-03-22 Online:2011-04-25 Published:2011-04-25
  • Supported by:

    国家自然科学基金(10671019, 10926056)和杭州电子科技大学校科研启动基金(KYS091507089)资助

摘要:

该文考虑由自适应直接方法求算子方程近似解的优化问题. 对核属于具有有界混合偏导Sobolev空间的第二类Fredholm积分方程, 确定了自适应逼近解误差的精确阶并给出了实现最优阶的算法.

关键词: 积分方程, 自适应直接方法, 具有有界混合偏导Sobolev空间

Abstract:

In this paper, the author  considers the problem of optimization of adaptive direct methods for approximate solution of operator
equations. For some classes of Fredholm integral equations of the second kind with kernels belonging to the Sobolev classes
with bounded mixed derivative, the author  determines the exact error orders on optimization of adaptive direct methods for approximate solution, and also gives an optimal algorithm in the sense of order.

Key words: Integral equations, Adaptive direct methods, Sobolev space with bounded mixed derivative

中图分类号: 

  • 41A65