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This Demonstration shows the graphic of the Green's function

related to the linear differential equation of order

, or

where

and with the following linear boundary conditions:

: periodic:

, initial:

, or final:

;

: periodic:

, Dirichlet:

or Neumann:

;

: periodic:

;

: periodic:

, simply supported beam:

, or clamped beam

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 an arbitrary interval

Reference

[1] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, New York-Toronto-London: McGraw–Hill, 1955.

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Green's Function