Green's Functions with Reflection Conditions
This Demonstration plots the Green’s function for the linear differential equation with reflection of order 1,[more]
and order ,
where you can vary the parameters and . These equations are coupled with one of the following linear boundary conditions:
initial condition: ,
final condition: ,
periodic condition: ,
antiperiodic conditions: .
Dirichlet conditions: ,
mixed conditions: ,
Neumann conditions: ,
periodic conditions: ,
antiperiodic conditions: ,
The solution of the boundary value problem (differential equation and boundary conditions) is given by .
In the code, the expression for the corresponding Green’s function is given for the arbitrary interval .[less]
The way to compute a Green's function for a problem with reflection is described in .
You can download a notebook for computing other Green's functions with reflection from .
 A. Cabada and F. Adrián F. Tojo, "An Algebraic Method of Obtaining the Green's Function for Some Reducible Functional Differential Equations." arxiv.org/abs/1411.5507.
 F. Adrián F. Tojo, A. Cabada, J. A. Cid, and B. Máquez-Villamarín, "Green's Functions with Reflection" from Wolfram Library Archive—A Wolfram Web Resource. library.wolfram.com/infocenter/MathSource/9087.