What is the idea behind Green's function? What does it do?
Apr 10, 2016 · 47 Green's function, also called a response function, is a device that would allow you to deal with linear boundary value problems (in the literature there are also Green's …
On the existence of Green's functions by Peter Lax
May 24, 2023 · My question is whether the existence of the Green's functions requires the differentiability of its regular part on the boundary. If yes, then does this paper show the …
General Solution of a Differential Equation using Green's Function
A very thorough treatment of the construction of Green's functions for second order ODEs can be found in the fantastic book Principles and Techniques of Applied Mathematics, by Bernard …
ordinary differential equations - Why must the Green's function …
Oct 10, 2025 · How can a single Green's function be used in both the inhomogeneous and homogeneous versions of a differential equation? Boundary conditions for Green's function? …
ordinary differential equations - What do Green's functions let you ...
Jul 7, 2025 · My question is: what do Green's functions let you find using the convolution: general or particular solutions? The Green's function found in (1), convolved, results in a general or in …
Green's function of a Markov Chain, and maybe of a Feller Process?
How are the Green's functions of a Markov chain related to the notion from PDE theory? These are the same: the Green function of a Markov chain is the Green function "from PDE theory" …
Green's function - Mathematics Stack Exchange
Jun 7, 2014 · You often find the name 'Green's function of the first kind' for this. Another problem which is of interest is prescribing the normal derivative of the solution at the boundary. For this, …
Examples of Greens functions for Laplace's equation with …
May 9, 2017 · Having redefined the Green's function, I'll give you an explicit expression in the case where $\Omega$ is a two-dimensional circular disk of radius $1$.
"Causality property" of Green's functions for the wave equation
Aug 26, 2024 · The classical representation of Green's functions for the wave equation for $n=1,2,3$ are obtained by Fourier transform methods. You can find these pretty easily just by …
A question on Green's functions & integral operators
Jul 10, 2015 · I'm fairly new to the concept of Green's functions, but from what I understand so far, they are a powerful tool for solving PDEs with boundary conditions. Given a differential …