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Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review

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Department of Mathematics, University of Salerno, 84084 Fisciano, Italy
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Department of Engineering and Computer Science and Mathematics, University of L’Aquila, Via Vetoio, Loc. Coppito, 67100 L’Aquila, Italy
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Author to whom correspondence should be addressed.
Axioms 2018, 7(3), 45; https://doi.org/10.3390/axioms7030045
Received: 27 April 2018 / Revised: 18 June 2018 / Accepted: 19 June 2018 / Published: 1 July 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
We present a collection of recent results on the numerical approximation of Volterra integral equations and integro-differential equations by means of collocation type methods, which are able to provide better balances between accuracy and stability demanding. We consider both exact and discretized one-step and multistep collocation methods, and illustrate main convergence results, making some comparisons in terms of accuracy and efficiency. Some numerical experiments complete the paper. View Full-Text
Keywords: Volterra integral equations; Volterra integro–differential equations; collocation methods; multistep methods; convergence Volterra integral equations; Volterra integro–differential equations; collocation methods; multistep methods; convergence
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MDPI and ACS Style

Cardone, A.; Conte, D.; D’Ambrosio, R.; Paternoster, B. Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review. Axioms 2018, 7, 45.

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