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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Published in:Physics reports Vol. 732; pp. 1 - 102
Main Author: Venturi, Daniele
Format: Journal Article
Language:English
Published: Elsevier B.V 18.02.2018
ISSN:0370-1573, 1873-6270
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Abstract 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.
AbstractList 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.
Author Venturi, Daniele
Author_xml – sequence: 1
  givenname: Daniele
  surname: Venturi
  fullname: Venturi, Daniele
  email: venturi@ucsc.edu
  organization: Department of Applied Mathematics and Statistics, University of California, Santa Cruz, United States
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Snippet The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf...
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