The numerical approximation of nonlinear functionals and functional differential equations

The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger–Dyson equations) and statistical physics (equations for generating functionals...

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Veröffentlicht in:Physics reports Jg. 732; S. 1 - 102
1. Verfasser: Venturi, Daniele
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 18.02.2018
ISSN:0370-1573, 1873-6270
Online-Zugang:Volltext
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Zusammenfassung:The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger–Dyson equations) and statistical physics (equations for generating functionals and effective Fokker–Planck equations). However, no effective numerical method has yet been developed to compute their solution. The purpose of this report is to fill this gap, and provide a new perspective on the problem of approximating numerically nonlinear functionals and the solution to functional differential equations.
ISSN:0370-1573
1873-6270
DOI:10.1016/j.physrep.2017.12.003