I am trying to write the following expression:
L[y[x]] = y'[x] - 1/h (a0 y[x - h] + a1 y[x] + a2 y[x + h])
I already saw an answer about something similar to this problem: f[y_]:=D[y,x]*2 and I understood the command of delayed definition. The problem is that in my case the argument x is important because I have to evaluate the function y in different points and this is giving me some issue. How I can write the formula in a proper way? Thanks in advance
I'm not exactly sure what you are trying to accomplish.
Is there any chance that this helps?
y[x_]:=Sin[x];
L[y_,x_] := (y'[z] - 1/h (a0 y[z - h] + a1 y[z] + a2 y[z + h]))/.z->x;
L[y,x]
L[y,2]
which returns
Cos[x] - (-(a0*Sin[h - x]) + a1*Sin[x] + a2*Sin[h + x])/h
and
Cos[2] - (a1*Sin[2] + a0*Sin[2 - h] + a2*Sin[2 + h])/h
That depends on z and perhaps x not previously having been assigned any values.
There are almost certainly other ways of doing that, like everything else in Mathematica.
Please test this VERY carefully before you even think of depending on this.