A representation for the solution of Fredholm integral equations
HTML articles powered by AMS MathViewer
- by H. H. Kagiwada, R. E. Kalaba and A. Schumitzky PDF
- Proc. Amer. Math. Soc. 23 (1969), 37-40 Request permission
Abstract:
This paper provides a new representation formula for the solution of Fredholm integral equations of the second kind. The formula has certain computational advantages over the usual representation involving the resolvent or the representation formula of Krein. As an application, the Bellman-Krein partial differential equation for the resolvent is derived.References
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Richard Bellman, Functional equations in the theory of dynamic programming. VII. A partial differential equation for the Fredholm resolvent, Proc. Amer. Math. Soc. 8 (1957), 435–440. MR 88666, DOI 10.1090/S0002-9939-1957-0088666-4
- M. G. Kreĭn, On a new method of solution of linear integral equations of first and second kinds, Dokl. Akad. Nauk SSSR (N.S.) 100 (1955), 413–416 (Russian). MR 0073060 H. Kagiwada and R. Kalaba, An initial-value method for Fredholm integral equations of convolution type, The RAND Corporation, RM-5186-PR, 1966. H. Kagiwada, R. Kalaba and S. Ueno, Evaluation of functionals of solutions of Fredholm integral equations with displacement kernels, The RAND Corporation, RM-5459-PR, 1967. V. V. Sobolev, A treatise on radiative transfer, Van Nostrand, Princeton, N. J., 1963. H. Kagiwada and R. Kalaba, A new initial-value method for internal intensities in radiative transfer, Astrophys. J. 147 (1967), 301-309.
- Sueo Ueno, The invariant imbedding method for transport problems. II. Resolvent in photon diffusion equation, J. Math. Anal. Appl. 3 (1961), 361–372. MR 165932, DOI 10.1016/0022-247X(61)90063-4
- H. H. Kagiwada and R. E. Kalaba, An initial-value method suitable for the computation of certain Fredholm resolvents, J. Mathematical and Physical Sci. 1 (1967), no. 1-2, 109–122. MR 225513
- H. H. Kagiwada, R. E. Kalaba, and A. Schumitzky, An initial-value method for Fredholm integral equations, J. Math. Anal. Appl. 19 (1967), 197–203. MR 215548, DOI 10.1016/0022-247X(67)90032-7
- Alan Schumitzky, On the equivalence between matrix Riccati equations and Fredholm resolvents, J. Comput. System Sci. 2 (1968), 76–87. MR 241918, DOI 10.1016/S0022-0000(68)80005-4
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 23 (1969), 37-40
- MSC: Primary 45.11
- DOI: https://doi.org/10.1090/S0002-9939-1969-0246057-5
- MathSciNet review: 0246057