Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

Details Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

2011-12-20

arxiv.org/abs/1112.4649v1

J. Comput. Appl. Math. 235 (2011), no. 12, 3661-3672

Mathematics

Numerical Analysis

18 pages, 4 figures

Scientific paper

10.1016/j.cam.2011.02.026

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.

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