Next Article in Journal
Introduction to Special Issue: New Trends in Fuzzy Set Theory and Related Items
Next Article in Special Issue
Efficient BEM-Based Algorithm for Pricing Floating Strike Asian Barrier Options (with MATLAB® Code)
Previous Article in Journal
Quantiles in Abstract Convex Structures
Previous Article in Special Issue
On the Analysis of Mixed-Index Time Fractional Differential Equation Systems
Article Menu

Export Article

Open AccessReview
Axioms 2018, 7(2), 36; https://doi.org/10.3390/axioms7020036

Line Integral Solution of Differential Problems

1
Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
2
Dipartimento di Matematica, Università di Bari, Via Orabona 4, 70125 Bari, Italy
*
Author to whom correspondence should be addressed.
Received: 4 May 2018 / Revised: 27 May 2018 / Accepted: 28 May 2018 / Published: 1 June 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
View Full-Text   |   Download PDF [407 KB, uploaded 1 June 2018]   |  

Abstract

In recent years, the numerical solution of differential problems, possessing constants of motion, has been attacked by imposing the vanishing of a corresponding line integral. The resulting methods have been, therefore, collectively named (discrete) line integral methods, where it is taken into account that a suitable numerical quadrature is used. The methods, at first devised for the numerical solution of Hamiltonian problems, have been later generalized along several directions and, actually, the research is still very active. In this paper we collect the main facts about line integral methods, also sketching various research trends, and provide a comprehensive set of references. View Full-Text
Keywords: conservative problems; Hamiltonian problems; energy-conserving methods; Poisson problems; Hamiltonian Boundary Value Methods; HBVMs; line integral methods; constrained Hamiltonian problems; Hamiltonian PDEs; highly oscillatory problems conservative problems; Hamiltonian problems; energy-conserving methods; Poisson problems; Hamiltonian Boundary Value Methods; HBVMs; line integral methods; constrained Hamiltonian problems; Hamiltonian PDEs; highly oscillatory problems
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

Brugnano, L.; Iavernaro, F. Line Integral Solution of Differential Problems. Axioms 2018, 7, 36.

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