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From: Allamarein on 1 Mar 2010 05:19
I compiled this program to solve a ODEs, but it is not able to
converge. Someone can suggest a method?

F = 26 *10^5;
\[Mu] = 5.9742 *10^24 *6.67428* 10^-11;
Isp = 290;
m = F/(9.81 Isp);
GLOW = 80000 + 23805 + 9000 + 370 + 8500 + 2556 + 1056 + 413 + 1300 +
385;
tb = 80000/m;
r0 = 6371;
\[Theta]0 = 85 Degree;
\[Gamma]0 = 85 Degree;
V0 = 100;
V = Sqrt[(r'[t]^2 + r[t]^2 \[Theta]'[t]^2)];
R = 1.44 Exp[-0.14 (r[t]/1000 - 6380)] V^2;
On[NDSolve::"ndcf"];
Off[NDSolve::"precw"];
NDSolve[{
r''[t] - r [t] \[Theta]'[t]^2 == (-M [t] \[Mu] +
r[t]^2 (F - R) Cos[\[Gamma][t] - \[Theta][t]])/(M[t] r[t]^2),
2 r'[t] \[Theta]'[t] +
r[t] \[Theta]''[t] == ((F - R) Sin[\[Gamma][t] - \[Theta][t]])/(
M [t] r[t]),
\[Gamma]'[
t] == -\[Mu] (-Sin[\[Gamma][t] - \[Theta][t]])/(r[t]^2 V) ,
M'[t] == -m,
r[0] == r0,
\[Gamma][0] == \[Gamma]0,
\[Theta][0] == \[Theta]0,
r'[0] == V0 Cos[\[Gamma]0 - \[Theta]0],
\[Theta]'[0] == r0 V0 Sin[\[Gamma]0 - \[Theta]0],
M[0] == GLOW},
{r[t], \[Theta][t], \[Gamma][t], M[t]},
{t, 0, tb}, MaxSteps -> 1000000, AccuracyGoal -> 25,
PrecisionGoal -> 40, WorkingPrecision -> 50];

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