Analysis of collocation solutions for nonstandard Volterra integral equations

In this paper, we study the existence, uniqueness and regularity properties of solutions for the nonstandard Volterra integral equation u(t) = g(t) + ∫ t 0 K (t, s, u(t), u(s)) ds, t ∈ [0, T ]. We then present a collocation method to solve this equation, and analyse the convergence and superconvergence of piecewise polynomial collocation approximations. We also illustrate the theoretical results by extensive numerical experiments.

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