Degenerate kernel method for Hammerstein equations
HTML articles powered by AMS MathViewer
- by Hideaki Kaneko and Yuesheng Xu PDF
- Math. Comp. 56 (1991), 141-148 Request permission
Abstract:
The classical method of the degenerate kernel method is applied to numerically solve the Hammerstein equations. Several numerical examples are given to demonstrate the effectiveness of the current method. A brief discussion of a number of methods to decompose the kernel is also included.References
- Lothar Bamberger and Günther Hämmerlin, Spline-blended substitution kernels of optimal convergence, Treatment of integral equations by numerical methods (Durham, 1982) Academic Press, London, 1982, pp. 47–57. MR 755341
- Hideaki Kaneko, A projection method for solving Fredholm integral equations of the second kind, Appl. Numer. Math. 5 (1989), no. 4, 333–344. MR 1005380, DOI 10.1016/0168-9274(89)90014-7
- Sunil Kumar and Ian H. Sloan, A new collocation-type method for Hammerstein integral equations, Math. Comp. 48 (1987), no. 178, 585–593. MR 878692, DOI 10.1090/S0025-5718-1987-0878692-4
- Sunil Kumar, A discrete collocation-type method for Hammerstein equations, SIAM J. Numer. Anal. 25 (1988), no. 2, 328–341. MR 933728, DOI 10.1137/0725023
- L. J. Lardy, A variation of Nyström’s method for Hammerstein equations, J. Integral Equations 3 (1981), no. 1, 43–60. MR 604315
- Larry L. Schumaker, Spline functions: basic theory, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1981. MR 606200
- F. G. Tricomi, Integral equations, Dover Publications, Inc., New York, 1985. Reprint of the 1957 original. MR 809184
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 56 (1991), 141-148
- MSC: Primary 65R20; Secondary 45L05
- DOI: https://doi.org/10.1090/S0025-5718-1991-1052097-9
- MathSciNet review: 1052097