Solve a coupled second order differential equations of two variables?

Questions
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1

Hello friends!!
I want to solve coupled two second order and one first order differential equations of two variables
and want to plot 3D graph. My code is attached and it is giving errors.
Kindly help me to remove the errors.

ques - Copy.nb (27.3 KB)

2

The code contains errors related to the formatting of the input data. Functions depend on r as on the parameter. Assuming that all functions depend only on one variable \xi , we find the system of the ODE, in which we make one change in order to eliminate the solution in the complex plane: B=1+Qd 2 \pi (k1ro1)^2 f3[\xi]
As a result, we find

w1 = 2.126*10^15;
w2 = 4.270*10^15;
wp = 1.78*10^13;
m = 9.1*10^-28;
c = 3*10^10;
e = 4.8*10^-10;
ro1 = 40*10^-4;
ro2 = 40*10^-4;
wr = (wp*ro1)/c;
l = 0.234;
k1 = 70861.75 + 0.0755*I;
eo1 = 1 - wp^2/w1^2;
eo2 = 1 - wp^2/w2^2;

Qd = 6.12*10^(-11) - 8.9*I*10^(-10);
eq = {f1''[\[Xi]] - 1/
     f1[\[Xi]]^3 + (wr^2*f1[\[Xi]])/
      2*(0.1/f1[\[Xi]]^4 + 0.2/(ro2^2*f2[\[Xi]]^4))*
      Exp[(-0.1/f1[\[Xi]]^2 - 0.2/f2[\[Xi]]^2)] == 0, 
   f2''[\[Xi]] - 1/
     f2[\[Xi]]^3 + (wr^2*eo1*f2[\[Xi]]*0.5)/(
      2*eo2)*(0.1/f1[\[Xi]]^4 + 0.2/(ro2^2*f2[\[Xi]]^4))*
      Exp[(-0.1/f1[\[Xi]]^2 - 0.2/f2[\[Xi]]^2)] == 0, 
   f3'[\[Xi]] + (Exp[-r^2/f1[\[Xi]]^2]*Exp[-1/(2*f2[\[Xi]]^2)])/(
     f1[\[Xi]]^2*f2[\[Xi]]) == 0};
bc = {f1[0] == 1, f1'[0] == 0, f2[0] == 10, f2'[0] == 0, f3[0] == 0};
F3 = ParametricNDSolveValue[{eq, bc}, f3, {\[Xi], 0, 15}, {r}];
F1 = ParametricNDSolveValue[{eq, bc}, f1, {\[Xi], 0, 15}, {r}];
F2 = ParametricNDSolveValue[{eq, bc}, f2, {\[Xi], 0, 15}, {r}];

{Plot[Evaluate[Table[F1[r][\[Xi]], {r, 0, 3, 1}]], {\[Xi], 0, 2}, 
  PlotRange -> All, AxesLabel -> {"\[Xi]", "f1"}], 
 Plot[Evaluate[Table[F2[r][\[Xi]], {r, 0, 3, 1}]], {\[Xi], 0, 2}, 
  PlotRange -> All, AxesLabel -> {"\[Xi]", "f2", ""}], 
 Plot[Evaluate[
   Table[Abs[1 + Qd*k1^2*2*Pi*(ro1)^2*F3[r][\[Xi]]], {r, 
     0, .5, .1}]], {\[Xi], 0, 2}, PlotRange -> All, 
  AxesLabel -> {"\[Xi]", ""}, PlotLabel -> "normalized intensity", 
  PlotLegends -> Automatic]}

3ode.png
3ode.png1256×281 53.2 KB

From the above figure we see that only f3 and, accordingly, B depends on the parameter r.

Plot3D[Evaluate[Abs[1 + Qd*k1^2*2*Pi*(ro1)^2*F3[r][\[Xi]]]], {\[Xi], 
  0, 2}, {r, 0, 1}, PlotRange -> All, AxesLabel -> {"\[Xi]", "r", ""},
  PlotLabel -> "normalized intensity", PlotLegends -> Automatic, 
 ColorFunction -> "RustTones"]

3ode1.png
3ode1.png694×433 116 KB

3

Thanks sir for your answer. I will make changes in my code as per your suggestions and try to get the required results

4

Sir,
I want to plot 3D graph of B with zeta and r.

5

What is the problem? I edited the code, added 3D figure.

6

Sir,
Actually i have also tried the same command but, i am not able to get the output. My code is attached below.

Ans2.nb (16.1 KB)

7

Code dosen’t work ,because you’re using the older version of Mathematica 7.0.

You must upgrade to a newer version probably at least 11 .

8

Unfortunately, I can not adapt the code for the old version of Mathematica.

9

Sure sir. I got your point. Thanks you so much

10

Thanks Sir for your help. I will upgrade to higher version.