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Student Support Forum: 'NDSolve::ndsz' topicStudent Support Forum > General > "NDSolve::ndsz"

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Gausstein
12/22/11 11:24am

Greetings,
I have a problem solving two coupled differential equations using NDSolve.
The following message appears: "NDSolve::ndsz: At t == -0.008080592178665635`,
step size is effectively zero; singularity or stiff system suspected. >>"

Can NDSolve actually solve these equations? or should I better try another
program?
I have tried everything!!!
I just need to know if it is possible to solve this equations with
Mathematica.
The code used is the following:

*********************************************************************************************************

H0 = 1/5000000;
m = 3/500000000;
A = 1/10^2;
V0 = 3 H0^2;
V0a = V0 - 1/2 A m^2 (2^(2 - 18 (1 - (7 Sqrt[51])/50)) 5^(2 - 21 (1 - (7
Sqrt[51])/50)));

ti = -(11/10);
tf = -Exp[-10];
V[t_] := V0 + 1/2 m^2 phi[t]^2 + UnitStep[t + 1] (-V0 + V0a + 1/2 A m^2
phi[t]^2)

value1 = 2^(1 - 21/2 (1 - (7 Sqrt[51])/50)) 5^(1 - 12 (1 - (7 Sqrt[51])/50))
11^(3/2 (1 - (7 Sqrt[51])/50));
value2 = -3 2^(1 - 21/2 (1 - (7 Sqrt[51])/50)) 5^(2 - 12 (1 - (7 Sqrt[51])/50)
) 11^(3/2 (1 - (7 Sqrt[51])/50) -
1) (1 - (7 Sqrt[51])/50);

temp = NDSolve[{

Derivative[1][a][t]/a[t]^2 ==Sqrt[1/3 (1/2 (Derivative[1][phi][t]/a[t])^2 +
V[t])],
Derivative[2][phi][t] + 2 Derivative[1][a][t]/a[t] Derivative[1][phi][t] +
m^2 a[t]^2 phi[t] (1 + A UnitStep[t + 1]) == 0,
a[ti] == -1/(H0 ti),

phi[ti] == value1,

phi'[ti] == value2},

{a, phi}, {t, ti, tf}, MaxSteps -> \[Infinity], InterpolationOrder -> All]

***************************************************************************************************************

I know it looks pretty messy, but once it is copied into the Notebook (and if
it is converted into StandardForm) it gets clearer.
I really need help!!!!!!!!!!!!! What should I do?
Thanks a lot!!!

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