Next Article in Journal / Special Issue
Optimal B-Spline Bases for the Numerical Solution of Fractional Differential Problems
Previous Article in Journal / Special Issue
On Partial Cholesky Factorization and a Variant of Quasi-Newton Preconditioners for Symmetric Positive Definite Matrices
Article Menu

Export Article

Open AccessReview
Axioms 2018, 7(3), 45; https://doi.org/10.3390/axioms7030045

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

1
Department of Mathematics, University of Salerno, 84084 Fisciano, Italy
2
Department of Engineering and Computer Science and Mathematics, University of L’Aquila, Via Vetoio, Loc. Coppito, 67100 L’Aquila, Italy
*
Author to whom correspondence should be addressed.
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)
Full-Text   |   PDF [335 KB, uploaded 1 July 2018]   |  

Abstract

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

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.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top