Generic Partial Differential Equations may yield arbitrary functions in
their solutions.
When matching this generic solutions to initial or boundary conditions, we
get a functional equation: that is an equation whose variable is a function
(without derivatives).
If the function to be found has
On Mon, May 27, 2013 at 12:14 PM, F. B. wrote:
> Generic Partial Differential Equations may yield arbitrary functions in
> their solutions.
>
> When matching this generic solutions to initial or boundary conditions, we
> get a functional equation: that is an equation whose variable is a function
>
Wolfram Mathematica has RSolve:
http://reference.wolfram.com/mathematica/ref/RSolve.html
It is mainly used to solve recurrence equations, though it is able to
accept functional equations too.
Wikipedia on recurrence equations:
http://en.wikipedia.org/wiki/Recurrence_relation
On Monday, May 27
SymPy also has rsolve(), but it only solves recurrence relations.
Aaron Meurer
On May 27, 2013, at 4:23 PM, "F. B." wrote:
Wolfram Mathematica has RSolve:
http://reference.wolfram.com/mathematica/ref/RSolve.html
It is mainly used to solve recurrence equations, though it is able to
accept funct
If the functional equation contains f(a) and f(b), it can be reduced to a
recurrence formula by
k (x + 1) = a
k x = b
which is
k = a - b
x = b / (a - b)
now the new function g(x) = f(k*x) displays the same equation as a
recurrence equation [ g(x) = f(b), g(x+1) = f(a) ].
That was just an att
I guess a recurrence relation is a special case of a functional
equation. I didn't consider that a functional equation might be
transformable to a recurrence relation via a change of variable.
I'm not sure how well your way works. If you take the classical
functional equation f(a + b) = f(a)*f(b
