期刊文献+

L^1空间中第二类Fredholm积分方程数值解法探究 被引量:14

One Research of Numerical Solution Methods of Fredholm Integral Equation of the Second Kind in L^1 Space
原文传递
导出
摘要 在L^1空间中对第二类Fredholm积分方程提出了一种求其数值解的算法,证明了算法的收敛性,并给出相应的误差估计.数值算例进一步验证了算法的合理性. Another algorithm for the numerical solution of Fredholm integral equation of the second kind in L1 space is discussed. The convergence of the algorithm is proved and the corre- sponding error estimation is given. Finally, a specific numerical example is shown to demonstrate the rationality of the proposed algorithm.
出处 《数学的实践与认识》 CSCD 北大核心 2013年第1期244-249,共6页 Mathematics in Practice and Theory
基金 黑龙江省自然科学基金项目(A201101)
关键词 FREDHOLM积分方程 离散化方法 紧算子 Fredholm integral equation discretization method compact opertor
  • 相关文献

参考文献5

  • 1Alpert B,Beylkin G,Coifman R,Rokhlin V. Wavelets for the fast solution of second-kind integral equations[J].SIAM Journal on Scientific Computing,1993,(14):159-184.
  • 2Atkinson K E. A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind[M].Philadelphia,PA:SIAM,1976.
  • 3Xie W J,Lin F R. A fast numerical solution method for two dimensional Fredholm integral equations of the second kind[J].Applied Numerical Mathematics,2009,(59):9-19.
  • 4M.Thamban Nair. Linear Operator Equations:Approximation and Regularization[M].World Scientific Pubishing Company,2009.
  • 5沈以淡.积分方程[M]北京:北京理工大学出版社,1992.

同被引文献41

  • 1刘唐伟,应正卫,吴志强.第二类非线性Fredholm型积分方程数值解[J].东华理工学院学报,2005,28(3):294-296. 被引量:3
  • 2赵明皞,李冬霞,沈亚鹏.三维横观各向同性介质界面裂纹的边界积分方程方法[J].应用数学和力学,2005,26(12):1394-1400. 被引量:6
  • 3范天佑,孙竹凤.一类二维对偶积分方程的解及其应用[J].应用数学和力学,2007,28(2):225-230. 被引量:1
  • 4朱广田,林群.迁移方程离散纵标法的收敛性[J].应用数学学报,1982,5(1):53-59.
  • 5M.Thambannair. Linear Operator Equations [M]. World Scientific, 2009.
  • 6P.W.Hemker, H.Schippers. Multiple grid methods for the solution of Fredholm integral equations of the 2nd kind [J]. Math Comput, 1981, 36(2): 215-232.
  • 7R.Piessens. Computing integral transforms and solving integral equations using Chebyshev poly- nomial approximations [J]. J Comp Appl Math, 2000, 121(3): 113-124.
  • 8M.Thamban Nair: Linear Operator Equations: Approximation and Regularization [M]. Singapore: World Scientific Publishing Company, 2009.
  • 9Cao Yanzhao, Huang Min, etc. Hybrid collocation methods for Fredholm integral equations with weakly singular kernels [J]. Applied Numerical Mathematics, 2007, 57(3): 549-561.
  • 10W.J. Xie, F.R. Lin. A fast numerical solution method for two dimensional Fredholm integral equations of the second kind[J]. Appl. Numer. Math, 2009, 55(2): 9-19.

引证文献14

二级引证文献22

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部