Abstract
It is established that a recently developed initial-value method for solving a family of Fredholm integral equations is equivalent to an initial-value version of a classical method based on solving a set of linear equations. This enables the establishment of the convergence of the numerical method.
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References
Kalaba, R., andZagustin, E.,Reduction of Fredholm Integral Equations to Cauchy Systems, University of Southern California, 1970.
Golberg, M. A.,Initial Value Methods in the Theory of Fredholm Integral Equations, Journal of Optimization Theory and Applications, Vol. 9, No. 2, 1972.
Hille, E.,Lectures in Ordinary Differential Equations, Addison-Wesley Publishing Company, Reading, Massachusetts, 1969.
Additional Bibliography
Casti, J., Kagiwada, H., Kalaba, R., andUeno, S.,Reduction of Fredholm Integral Equations to Cauchy Systems, University of Southern California, Technical Report No. 70-19, 1970.
Kalaba, R., andRuspini, E.,Reduction of the Dirichlet Problem to an Initial-Value Problem, University of Southern California, 1970.
Lovitt, W. V.,Linear Integral Equations, Dover Publications, New York, 1952.
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Communicated by R. E. Kalaba
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Golberg, M. Initial-value methods in the theory of Fredholm integral equations: II. J Optim Theory Appl 9, 426–432 (1972). https://doi.org/10.1007/BF00934741
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DOI: https://doi.org/10.1007/BF00934741