I'm trying to set the derivative of a function to zero at a specified point. This will act as an initial condition for an algorithm I'm writing: so I'm specifying the value of the function at x=0, and I'm specifying the value of the slope of the function at x=0. The function is u[n, x] and is unknown. The algorithm, based on Adomian decomposition method, will solve a nonlinear differential equation for this u-function.
Clear[u]
u /: D[u[n_, x_], x_] := 0
UpValues[u];
D[u[n, x], x] == 0
It gives the right output -- says it's True.
The problem I'm having is other queries say they are True when they shouldn't be:
D[u[n, x], 0] == 0 \\True
D[u[n, 0], 0] == 0 \\True
This is a somewhat duplicate of a question here, which is asked in a broader sense: How to set the derivative of a function to zero?
Ideally, what should happen is based on modifying this line of code:
u /: (D[u[n_, x_], x_] := 0)/.x->0
The result would be:
(D[u[n, x], x] == 0)/.x->0 \\True
(D[u[n, x], x] == 0)/.x->5 \\False or indeterminate
Thank you for any tips.
Derivative[]instead?u /: Derivative[0, 1][u][n_, x_] := 0. – J. M.'s missing motivation Jul 07 '16 at 23:36uis too deeply nested in the expression, so it won't work. Every time I thinkUpValuesis the solution to one of my problems, I get this error. – march Jul 07 '16 at 23:47Derivative[0, 1][u][n_, x_] := 0should have to suffice. – J. M.'s missing motivation Jul 07 '16 at 23:48Derivative[0, 1][u][n_, 0] := 0. – Michael E2 Jul 08 '16 at 00:33