Functional differential equations of Peano-Baker type
Authors:
R. C. Allen Jr. and W. T. Kyner
Journal:
Quart. Appl. Math. 31 (1974), 417-428
MSC:
Primary 34K05; Secondary 45B05
DOI:
https://doi.org/10.1090/qam/450737
MathSciNet review:
450737
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Abstract: The application of the moment method to a class of Fredholm integral equations leads to the study of both an infinite system of ordinary differential equations and a functional differential equation. Sufficient conditions are given that the solution to a truncated system of differential equations approximates the solutions to the original problem. A numerical algorithm for constructing approximate solutions is discussed.
- Richard C. Allen Jr., On the numerical solution of a certain class of non-linear Cauchy problems arising from intergral equation theory, Computing (Arch. Elektron. Rechnen) 7 (1971), 13–16. MR 290604, DOI https://doi.org/10.1007/bf02279937
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
- G. M. Wing, On certain Fredholm integral equations reducible to initial value problems, SIAM Rev. 9 (1967), 655–670. MR 227718, DOI https://doi.org/10.1137/1009107
R. C. Allen, Jr., On the numerical solution of a certain class of non-linear Cauchy problems arising from integral equation theory, Computing 7, 13–16 (1971)
E. L. Ince, Ordinary differential equations, Dover, New York, 1944
G. M. Wing, On certain Fredholm integral equations reducible to initial value problems, SIAM Review 9, 655–670 (1967)
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Article copyright:
© Copyright 1974
American Mathematical Society
