Computing Floquet transition matrix

[Nesrine]

hi ,

I need to create a program on mathématica 8 to study the stability of my system using Floquet transition matrix .

to compute the Floquet transition matrix I made this program based on a fourth order Runge Kutta integration :

X1[t_] = {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t] , x7[t], x8[t],
x9[t], x10[t], x11[t], x12[t]};
system1 = MapThread[#1 == #2 &, {X1'[t], A.X1[t]}];
X2[t_] = {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t] , x7[t], x8[t],
x9[t], x10[t], x11[t], x12[t]};
system2 = MapThread[#1 == #2 &, {X2'[t], A.X2[t]}];
X3[t_] = {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t] , x7[t], x8[t],
x9[t], x10[t], x11[t], x12[t]};
system3 = MapThread[#1 == #2 &, {X3'[t], A.X3[t]}];
X4[t_] = {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t] , x7[t], x8[t],
x9[t], x10[t], x11[t], x12[t]};
system4 = MapThread[#1 == #2 &, {X4'[t], A.X4[t]}];


CRK4[]["Step"[rhs_, t_, h_, y_, yp_]] :=
Module[{k0, k1, k2, k3}, k0 = h yp;
k1 = h rhs[t + h/2, y + k0/2];
k2 = h rhs[t + h/2, y + k1/2];
k3 = h rhs[t + h, y + k2];
{h, (k0 + 2 k1 + 2 k2 + k3)/6}]

CRK4[___]["DifferenceOrder"] := 4

dstep1 = NDSolve[{system1, x1[0] == 1,
x2[0] == x3[0] == x4[0] == x5[0] == x6[0] == x7[0] == x8[0] ==
x9[0] == x10[0] == x11[0] == x12[0] == 0}, {x1, x2, x3, x4, x5,
x6, x7, x8, x9, x10, x11, x12}, {t, 0, 2 \[Pi]},
Method -> {"DoubleStep", Method -> CRK4}];
dstep2 = NDSolve[{system2, x2[0] == 1,
x1[0] == x3[0] == x4[0] == x5[0] == x6[0] == x7[0] == x8[0] ==
x9[0] == x10[0] == x11[0] == x12[0] == 0}, {x1, x2, x3, x4, x5,
x6, x7, x8, x9, x10, x11, x12}, {t, 0, 2 \[Pi]},
Method -> {"DoubleStep", Method -> CRK4}];
dstep3 = NDSolve[{system3, x3[0] == 1,
x1[0] == x2[0] == x4[0] == x5[0] == x6[0] == x7[0] == x8[0] ==
x9[0] == x10[0] == x11[0] == x12[0] == 0}, {x1, x2, x3, x4, x5,
x6, x7, x8, x9, x10, x11, x12}, {t, 0, 2 \[Pi]},
Method -> {"DoubleStep", Method -> CRK4}];
dstep4 = NDSolve[{system4, x4[0] == 1,
x1[0] == x2[0] == x3[0] == x5[0] == x6[0] == x7[0] == x8[0] ==
x9[0] == x10[0] == x11[0] == x12[0] == 0}, {x1, x2, x3, x4, x5,
x6, x7, x8, x9, x10, x11, x12}, {t, 0, 2 \[Pi]},
Method -> {"DoubleStep", Method -> CRK4}];

and after that I get my transition matrix by using the solutions as the column.

The problem is that I don't get the expected result , so I'm wondering if my understanding of the method is correct or not.

If someone know how to compute Floquet transition matrix in mathematica 8 , I'll be very greatfull

thxx

 

[Nesrine]

I heard that a fourth order Runge Kutta integration procedure with Gill coefficients is the solution to my problem...the thing is that I don't know how to program this on mathématica

Can you help me please ??

Thanks