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


  • 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 summarizes TFC, a mathematical procedure to obtain constrained expressions. These are functionals representing all functions satisfying a set of linear constraints. These functionals contain a free function, g(x), representing the unknown function to optimize. Two numerical approaches are shown to numerically estimate g(x). The first models g(x) as a linear combination of a set of basis functions, such as Chebyshev or Legendre orthogonal polynomials, while the second models g(x) as a neural network. Meaningful problems are provided. In all numerical problems, the proposed method produces very fast and accurate solutions.

published proceedings


altmetric score

  • 0.5

author list (cited authors)

  • De Florio, M., Schiassi, E., D'Ambrosio, A., Mortari, D., & Furfaro, R.

citation count

  • 6

complete list of authors

  • De Florio, Mario||Schiassi, Enrico||D'Ambrosio, Andrea||Mortari, Daniele||Furfaro, Roberto

publication date

  • January 2021