I am developing a code which uses NDSolve to find solutions to two sets of two simultaneous differential equations, I would like to use a Do loop or a For loop to change some variables and repeat the calculations, to find the point where the sets diverge, however if I use a Do loop or a For loop, even without changing any other information, for instance, using a Do loop to do the calculations only once, NDSolve no longer works.
m = 9.1*10^-28; (*Mass of Electron in g*)(*Initialising constants, \
starting with universal constants*)
c = 3*10^10;(*Speed of light in cm/s*)
e = 4.8*10^-10;(*Electron charge in StatColoumb*)
\[Lambda] = 10^-4;(*Wavelength of laser in cm*)
r0 = 30*10^-4;(*Spot size in cm*)
n0 = 6*10^17;(*Electron density in cm^-3*)
energy = 10^5;(*Energy of laser pulse in erg*)
FWHM = 100*10^-15;(*Full-width half maximum of power distribution in \
seconds*)
\[Tau] = FWHM/(2 Sqrt[Log[2]]) // N;(*Time Constant in seconds*)
\[Omega]0 = 2*Pi*c/\[Lambda];
\[Omega]p = Sqrt[4*Pi*(e^2)*n0/m];(*Plasma Frequency in rad.s^-1*)
kp = \[Omega]p/c // N;
\[Tau]p = 2*Pi/\[Omega]p;
vp = c (1 - (\[Omega]p/\[Omega]0)^2)^0.5;
kR = r0*kp;
kZ = kp*vp*\[Tau];
P0 = (energy/FWHM)*Sqrt[2*Log[2]/Pi];(*Peak Power in erg/s*)
I0 = 2 P0/(Pi*r0^2);(*Peak Intensity in erg/(cm^2/s)*)
a0 = Sqrt[(2/(c*Pi))*(\[Lambda]*e/(m*c^2))^2*I0];(*Amplitude constant*)
asquared1[Z_, R_, T_] :=
a0^2*Exp[-(((Z - T)/kZ)^2)]*Exp[-2 ((R/kR)^2)];
Tmin = -20;
Tmax = 20;
Zmin = 0;
Zmax = 0.1;
Rmin = -0.1;
Rmax = 0.1;
T0 = -20;
Do[
s = NDSolve[{D[
u1[Z, R, T], {T, 2}]*(1 + 1.5*D[u1[Z, R, T], T]^2 +
0.5*D[v1[Z, R, T], T]^2) + u1[Z, R, T] -
D[v1[Z, R, T], T]*D[u1[Z, R, T], T]*v1[Z, R, T] == -0.5*
D[asquared1[Z, R, T], R],
D[v1[Z, R, T], {T, 2}]*(1 + 1.5*D[v1[Z, R, T], T]^2 +
0.5*D[u1[Z, R, T], T]^2) + v1[Z, R, T] -
D[u1[Z, R, T], T]*D[v1[Z, R, T], T]*u1[Z, R, T] == -0.5*
D[asquared1[Z, R, T], Z],
(D[u1[Z, R, T], T] /. T -> T0) == 0, v1[Z, R, T0] == 0,
u1[Z, R, T0] == 0, (D[v1[Z, R, T], T] /. T -> T0) == 0}, {u1,
v1}, {Z, Zmin, Zmax}, {R, Rmin, Rmax}, {T, Tmin, Tmax},
MaxSteps -> Infinity, MaxStepSize -> {0.1, 0.1, 0.1},
Method -> "ExplicitRungeKutta"]
First[NMaximize[{v1[0, 0, T] /. s[[1]], 10 < T < 20}, T]]
, {1}]
Removing the Do loop, the code works, but if I add it or a For loop, it gives the errros NMaximize::nnum: and Thread::tdlen: Could anyone suggest where I'm going wrong? Thank you.
Sorry for any mistakes with formatting, this is my first time using this website.
