RICHARDSON EXTRAPOLATION OF ITERATED DISCRETE COLLOCATION METHOD FOR EIGENVALUE PROBLEM OF A TWO DIMENSIONAL COMPACT INTEGRAL OPERATOR

다국어 초록 (Multilingual Abstract)

In this paper, we consider approximation of eigenelements of a twodimensional compact integral operator with a smooth kernel bydiscrete collocation and iterated discrete collocation methods. Bychoosing numerical quadrature appropriately, we obtain convergencerates for gap between the spectral subspaces, and also we obtainsuperconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardsonextrapolation to obtain further improved error bounds for theeigenvalues. Numerical examples are presentedto illustrate theoretical estimates.

참고문헌 (Reference)

1 K.E. Atkinson, "The numerical solution of integral equations of the second kind" Cambridge University Press 1997

2 M. Ahues, "Spectral computations for bounded operators" Chapman and Hall/CRC 2001

3 R.P. Kulkarni, "Spectral approximation using iterated discrete Galerkin method" 23 : 91-104, 2002

4 F. Chatelin, "Spectral approximation of linear operators" Academic Press 1983

5 G. Nelakanti, "Spectral approximation for integral operators" Indian Insitute of Technology 2003

6 J.E. Osborn, "Spectral approximation for compact operators" 29 : 712-725, 1975

7 Z. Chen, "Richardson extrapolation of iterated discrete projection methods for eigenvalue appoximation" 223 : 48-61, 2009

8 B.L. Panigrahi, "Richardson extrapolation of iterated discrete Galerkin method for eigenvalue problem of a two dimensional compact integral operator" 51 : 421-448, 2012

9 I.H. Sloan, "Iterated Galerkin method for eigenvalue problems" 13 : 753-760, 1976

10 Q. Lin, "Extrapolation of the iterated-collocation method for integral equations of the second kind" 27 : 1535-1541, 1990

11 G. Han, "Extrapolation of a discrete collocation-type method of Hammerstein equations" 61 : 73-86, 1995

12 S.D. Conte, "Elementary numerical analysis" Tata McGraw-Hill 2005

13 W. McLean, "Asymptotic error expansions for numerical solutions of integral equations" 9 : 373-384, 1989

14 G. Han, "Asymptotic Error Expansion of Two-Dimensional Volterra Integral Equation by Iterated Collocation" 61 : 269-285, 1994

15 E. Isaacson, "Analysis of Numerical Methods" John Wiley and Sons 1966

16 G. Nelakanti, "A degenerate kernel method for eigenvalue problems of compact integral operators" 27 : 339-354, 2007