Theory of Functional Connections Applied to Linear ODEs Subject to Integral Constraints and Linear Ordinary Integro-Differential Equations

• Published in: Mathematical and computational applications Vol. 26; no. 3; p. 65
• Main Authors: De Florio, Mario, Schiassi, Enrico, D’Ambrosio, Andrea, Mortari, Daniele, Furfaro, Roberto
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2021
• Subjects: Basis functions; Chebyshev approximation; Constraints; Differential equations; Extreme Learning Machine; Functionals; Integrals; integro-differential equations; Mathematical models; Neural networks; numerical methods; Ordinary Differential Equations; Physics; Polynomials; Theory of Functional Connections

This study shows how the Theory of Functional Connections (TFC) allows us to obtain fast and highly accurate solutions to linear ODEs involving integrals. Integrals can be constraints and/or terms of the differential equations (e.g., ordinary integro-differential equations). This study first summari...