The petrov-galerkin and iterated petrov-galerkin methods for second-kind integral equations

SIAM Journal on Numerical Analysis

Volumn 35, Issue 1, 1998, Pages 406-434

  Chen, Zhongying ^a   Xu, Yuesheng ^b  

^a SUN YAT SEN UNIVERSITY   (China)

^b NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

Regular pairs; The iterated Petrov Galerkin method; The Petrov Galerkin method

Indexed keywords

EID: 0001381725     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996297217     Document Type: Article

References (17)

1. [At1] K. E. ATKINSON, A Survey of Numerical Methods for Fredholm Integral Equations of the Second Kind, SIAM, Philadelphia, PA, 1976.
2. [At2] K. E. ATKINSON, A survey of boundary integral equation methods for the numerical solution of integral equations, in Numerical Solution of Integral Equations, M. Golberg, ed., Plenum, New York, 1990, pp. 1-34.
3. [At3] K. E. ATKINSON, Two-grid iteration methods for linear integral equations of the second kind on piecewise smooth surfaces in R3, SIAM J. Sci. Comput., 15 (1994), pp. 1083-1104.
4. [AP] K. E. ATKINSON AND F. POTRA, Projection and iterated projection methods for nonlinear integral equations, SIAM J. Numer. Anal., 24 (1987), pp. 1352-1373.
5. [AS] K. E. ATKINSON AND I. SLOAN, The numerical solution of the first kind logarithmickernel integral equations on smooth open arcs, Math. Comp., 56 (1991), pp. 119-139.
6. [C1] Z. CHEN, The error estimate of generalized difference method of 3rd-order Hermite type for elliptic partial differential equations, Northeast. Math. J., 8 (1992), pp. 127-135.
7. (C2] Z. CHEN, Superconvergence of generalized difference method for elliptic boundary value problem, Numer. Math. J. Chinese Univ., 3 (1994), pp. 163-171.
8. [KX] H. KANEKO AND Y. Xu, Superconvergence of the iterated Galerkin methods for Hammerstein equations, SIAM J. Numer. Anal., 33 (1996), pp. 1048-1064.
9. [KVZRS] M. A. KRANSNODEL'SKII, G. M. VAINIKKO, P. P. ZABREIKO, YA. B. RUTITSKII, AND V. YA. STETSENKO, Approximate Solution of Operator Equations, Wolters-Noordhoff, Groningen, the Netherlands, 1972.
10. [Kr] R. KRESS, Linear Integral Equations, Springer-Verlag, New York, 1989.
11. [LI] R. LI, On generalized difference method for elliptic and parabolic differential equation, in Proc. Symp. Finite Element Method between China and France, Feng Kang and J. L. Lions, eds., Science Press, Beijing, China, 1982, pp. 323-360.
12. [L2] R. LI, Generalized difference methods for a nonlinear Dirichlet problem, SIAM J. Numer. Anal., 24 (1987), pp. 77-88.
13. [LC] R. LI AND Z. CHEN, The Generalized Difference Method for Differential Equations, Jilin University Publishing House, Changchun, China, 1994.
14. [MPW] W. MCLEAN, S. PROESSDORF, AND W. L. WENDLAND, A full-discrete trigonometric collocation method, J. Integral Equations Appl., 5 (1993), pp. 103-129.
15. [S] I. SLOAN, Superconvergence, in Numerical Solution of Integral Equations, M. Golberg, ed., Plenum, New York, 1990, pp. 35-70.
16. [XZ1] Y. Xu AND Y. ZHAO, An extrapolation method for a class of boundary integral equations, Math. Comp., 65 (1996), pp, 587-610.
17. [XZ2] Y. Xu AND Y. ZHAO, Quadratures for boundary integral equations of the first kind with logarithmic kernels, J. Integral Equations Appl., 8 (1996), pp. 239-268.