Green’s function for differential operator
Assume we are given and we want to find such that
(1) |
Expression (1) is an example of initial value problem for an ordinary differential equation
. Let us
show, that (1) can be put into the framework of the definition for Green’s function.
-
1.
.
-
2.
. -
3.
Thus (1) can be written as an operator equation
(2) |
To find the Green’s function for (2) we proceed as follows:
where has the following form:
(3) |
Thus, function (3) is the Green’s function for the operator equation (2) and then for the problem (1).
Its graph is presented in Figure 1.
Title | Green’s function for differential operator![]() |
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Canonical name | GreensFunctionForDifferentialOperator |
Date of creation | 2013-03-22 14:43:39 |
Last modified on | 2013-03-22 14:43:39 |
Owner | mathforever (4370) |
Last modified by | mathforever (4370) |
Numerical id | 7 |
Author | mathforever (4370) |
Entry type | Example |
Classification | msc 34A99 |
Classification | msc 34A30 |