Green’s functions/fundamental solutions

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Presentation transcript:

Green’s functions/fundamental solutions Sept 20 Analytical solutions Green’s functions/fundamental solutions Jing-Rebecca Li Equipe DEFI, CMAP, Ecole Polytechnique Institut national de recherche en informatique et en automatique (INRIA) Saclay

Many exact solutions http://eqworld.ipmnet.ru/en/solutions/lpde.htm Linear Partial Differential Equations of Mathematical Physics Second-Order Parabolic Partial Differential Equations Second-Order Hyperbolic Partial Differential Equations Second-Order Elliptic Partial Differential Equations Other Second-Order Partial Differential Equations Higher-Order Partial Differential Equations

Heat equation

Heat equation

Heat equation

Heat equation

Heat equation

Heat equation

Heat equation

Laplace equation

In mathematics, a fundamental solution for a linear partial differential operator L is a formulation in the language of distribution theory of the older idea of a Green's function, which normally further addresses boundary conditions.

Analytical solutions/Green’s functions

PAUSE Time for a break