PDE approximation of large systems of differential equations

András Bátkai, Ágnes Havasi, Róbert Horváth, Dávid Kunszenti-Kovács, L. P. Simon

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A large system of ordinary differential equations is approximated by a parabolic partial differential equation with dynamic boundary condition and a different one with Robin boundary condition. Using the theory of differential operators with Wentzell boundary conditions and similar theories, we give estimates on the order of approximation. The theory is demonstrated on a voter model where the Fourier method applied to the PDE is of great advantage.

Original languageEnglish
Pages (from-to)147-163
Number of pages17
JournalOperators and Matrices
Volume9
Issue number1
DOIs
Publication statusPublished - Mar 1 2015

Fingerprint

System of Differential Equations
Approximation
Wentzell Boundary Conditions
Dynamic Boundary Conditions
Voter Model
Robin Boundary Conditions
Fourier Method
Order of Approximation
Parabolic Partial Differential Equations
System of Ordinary Differential Equations
Differential operator
Estimate

Keywords

  • Approximation theorems
  • C<inf>0</inf> -semigroups
  • Dynamics on networks
  • Finite differences

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Bátkai, A., Havasi, Á., Horváth, R., Kunszenti-Kovács, D., & Simon, L. P. (2015). PDE approximation of large systems of differential equations. Operators and Matrices, 9(1), 147-163. https://doi.org/10.7153/oam-09-08

PDE approximation of large systems of differential equations. / Bátkai, András; Havasi, Ágnes; Horváth, Róbert; Kunszenti-Kovács, Dávid; Simon, L. P.

In: Operators and Matrices, Vol. 9, No. 1, 01.03.2015, p. 147-163.

Research output: Contribution to journalArticle

Bátkai, A, Havasi, Á, Horváth, R, Kunszenti-Kovács, D & Simon, LP 2015, 'PDE approximation of large systems of differential equations', Operators and Matrices, vol. 9, no. 1, pp. 147-163. https://doi.org/10.7153/oam-09-08
Bátkai A, Havasi Á, Horváth R, Kunszenti-Kovács D, Simon LP. PDE approximation of large systems of differential equations. Operators and Matrices. 2015 Mar 1;9(1):147-163. https://doi.org/10.7153/oam-09-08
Bátkai, András ; Havasi, Ágnes ; Horváth, Róbert ; Kunszenti-Kovács, Dávid ; Simon, L. P. / PDE approximation of large systems of differential equations. In: Operators and Matrices. 2015 ; Vol. 9, No. 1. pp. 147-163.
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