The Numerical Approximation of Nonlinear Functionals and Functional Differential Equations
Numerical Analysis
2019-10-02 v3 Mathematical Physics
math.MP
Computational Physics
Fluid Dynamics
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 numerical approximation of nonlinear functionals and functional differential equations.
Cite
@article{arxiv.1604.05250,
title = {The Numerical Approximation of Nonlinear Functionals and Functional Differential Equations},
author = {Daniele Venturi},
journal= {arXiv preprint arXiv:1604.05250},
year = {2019}
}
Comments
142 pages, 41 figures