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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Vydáno v:Physics reports Ročník 732; s. 1 - 102
Hlavní autor: Venturi, Daniele
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 18.02.2018
ISSN:0370-1573, 1873-6270
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Popis
Shrnutí: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