The subject are LDE's with constant coefficients of the following form:
,
and being polynomials of given degrees.
1) I choose the , let it be .
2) I write down the following functions:
every such function satisfies the conditions below:
3) I put down both the source term and the solution function using a base , so that the right side of the equation becomes , and the solution becomes .
4) I make two additional matrices:
,
therefore
5) Finally I rewrite the initial equation:
eventually giving , which can be solved for .
Has such a method been described somewhere, or is it something new?
Thanks in advance