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Problem with NDSolve in Mathematica 9

Posted 10 years ago

I'm having trouble by solving the following differential equation in Mathematica 9 and 10, where the code works fine in version 7:

?p = 200*10^(-15); 
e = 1.60217653*10^(-19); 
me = 9.1093826*10^(-31); 
c = 2.99792458*10^(8); 
? = 8.854187817*10^(-12); 
h = 6.626*10^(-34); 
hbar = h/(2 Pi);  
? = 786*10^(-9);
n0 = 1.45; 
mred = 0.635*me ;
Eg = 7.5*e;
?r = 220*10^(-15);
? = (2 Pi c)/?;
k0 = (n0 ?/c);
rhocrit = (?*mred*?^2/(e^2));
H = 2*10^(4);
I0 = H*(2 Sqrt[Log[2]])/(?p Sqrt[Pi]);
Int1[t_] := I0*Exp[-4 Log[2] (t^2/?p^2)];
?[Int_] := (?/e)*Sqrt[(mred c n0 ? Eg)/(2 Int)];
?[Int_] := ?[Int]^2/(1 + ?[Int]^2);
?[Int_] := 1/(1 + ?[Int]^2);
?[Int_] := Pi^2/(2 EllipticK[?[Int]]*EllipticE[?[Int]]);
x[Int_] := (2 Eg)/(Pi hbar ? Sqrt[?[Int]])*EllipticE[?[Int]];
?[Int_] := IntegerPart[x[Int] + 1] - x[Int];
Q[Int_] := Sqrt[(Pi)/(2 EllipticK[?[Int]])] Sum[
Exp[-s Pi ((EllipticK[?[Int]] - 
       EllipticE[?[Int]])/(EllipticE[?[
        Int]]))] DawsonF[
  Sqrt[?[Int] (s + 2 ?[Int])]], {s, 0, 5}];
WPI[Int_] := If[10^(3) > Int, 0, (2 ?)/(9 Pi) *((? mred )/(hbar Sqrt[?[Int]]))^(3/2)*Q[Int]*
Exp[-Pi ((EllipticK[?[Int]] - 
      EllipticE[?[Int]])/(EllipticE[?[Int]]))*
  IntegerPart[x[Int] + 1]]];
Ekrit[t_] := Eg (1 + 1/(4 ?[Int1[t]]^2));
Ekin[t_] := Ekrit[t]/10;

s1 = NDSolve[{sol1'[t] == 
 WPI[Int1[
    t]] + (((k0 ? ((16 Pi ?^2 Sqrt[
              mred Ekin[t]^3])/(Sqrt[2]*e^4*
             sol1[t])))/(n0^2 rhocrit (1 + ?^2*(((16 Pi \
?^2 Sqrt[mred Ekin[t]^3])/(Sqrt[2]*e^4*sol1[t]))^2)))) sol1[
      t] Int1[t])/(Eg) - sol1[t]/?r, sol1[-3 ?p] == 1}, 
sol1, {t, -3.1 ?p, 4 ?p}];

In version 7 there are no error messages and with:

LogPlot[Evaluate[sol1[t]/.s1],{t,-2 ?p, 2?p}]

I get the expected result:

enter image description here

but using the newer version the kernel shuts down without giving an output. Anyone got an idea how to solve this problem?

POSTED BY: Peter Juergens
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