My functions are:
$$E_x[x,z,t] := \frac {\gamma E_0 (x - v t) } {(\gamma^2 (x - v t)^2 + z^2)^{3/2}}$$
$$I_x[x,z,t] := \int_0^{\infty} {e^{-e w} \sin(s w) E_x[x, z, t - w]} dw$$
with the proper real values of $\gamma$, e, s, E0 and v. Now I want to solve:
$$f_x[t] = I_x[f_x[t],1,t]$$
That is, in Mathematica terms:
NDSolve[{fx[t] == Ix[fx[t], 1, t], fx[0] == 0}, fx, {t, 0, 10}].
I've tried defining Ix as Ix[x_, z_, t_?NumberQ] But the result is:
NDSolve::ndfdmc: Computed derivatives do not have dimensionality consistent with the initial conditions.
I'm still new to Mathematica. If someone could help me, it will be appreciated.
The code looks like:
Ex[x_,z_,t_] := y E0 (x- v t) /(((y^2) ((x - v t)^2) + z^2)^1.5)
Ix[x_?NumericQ, z_, t_]:=NIntegrate[{(Exp[-e w]) (Sin[s w]) Ex[x,z,t-w]},{w,0,100}]
NDSolve[{gx'[t] == Ix[gx[t], b, t], gx[0] == 0}, gx, {t, -10, 10}]
Thankyou for your replies! In fact is not a findroot problem, i want to get x(t) as a function.
NDSolve? It looks like aFindRootsort of problem (where you fix all parameters except for x). – b.gatessucks Jan 18 at 8:29{ }button. – Mr.Wizard♦ Jan 21 at 20:06Ixreturns a list, which is whyNDSolvegives the error. You can click the little>>at the end of the error message to get documentation about the error. For this error it says "This message is generated when the equations for the derivatives give values with list structures that are not equivalent to the lists used in specifying the initial conditions.", which is exactly your problem. – Simon Woods Jan 21 at 22:42