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The Extragalactic Reference

By Kai (prc-jil) Zhang and Ran (prc-jil


Analysis of continuous collocation solutions for a kind of Volterra functional integral equations with proportional delay. (English summary) J. Comput. Appl. Math. 236 (2011), no. 5, 743–752. In the paper, a functional equation y(t) = b(t, y(qt)) + f(t), t ∈ (0, T), 0 < q < 1, and its perturbation, obtained by introducing the Volterra-type integral terms, y(t) = b(t, y(qt)) + f(t) + ∫ t 0 K0(t, s)y(s)ds + ∫ qt 0 K1(t, s)y(s)ds, are investigated. First, the existence, uniqueness and regularity of solutions for these equations are studied. Next, the convergence of the piecewise linear collocation method applied to their approximate solution is analyzed. For illustration of the theoretical results, some numerical examples are provided. Reviewed by Wojciech Mydlarczy

Year: 1995
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