Mark,

I would solve this problem by MATLAB ODE solvers. MATLAB has couple of ODE solvers such as ode45 that can be used to solve system of linear ODEs. The periodic coefficient, A(t), can be defined by two vectors. One vector contains the time intervals and the other corresponding values of A(t). You need to use interp1 command to allow the ODE solver evaluate A(t) at all the times. The implementation procedure for a similar problem is explained in the Example 3 in the following link:

http://www.mathworks.com/help/matlab/ref/ode45.html

Hope it helps.

Farzad

http://www.mathworks.com/help/matlab/ref/ode45.html

An interesting paper in this regard seems to be the following:

``FLOQUET THEORY AS A COMPUTATIONAL TOOL'', by Gerald Moore,

http://www.mathnet.or.kr/mathnet/paper_file/IClondon/Moore/floquet.pdf

that seems to go into considerable detail and, thus, could be used to write code.

@ Stam: That's a great reference!  Thanks.

you can consider the attached paper :

"A perturbative procedure based on the Lie-Deprit algorithm of

classical mechanics is proposed to compute analytic approximations to the

fundamental matrix of linear dierential equations with periodic coecients."

R. Mark Bradley,

Hi, Prof. 

If the coefficients are periodic, which means that the matrices are circulant, then Fast Fourier transform can be applied. Then one can apply linear multistep formula based ODE solver, my Master works might be helpful to your problems.

Not sure it is good recomendation, the papers abouvу are great,

But I think You can use (may be) Filon method, 

Try to find solution for new function that is slow chnging amplutude.

for example

d^2/dt^2 x+w^2(1+fi(t))x=0 with some conditions

if You change unknown function

x(t)=exp(iwt)y(t)

the equation for y(t) will be better for numerical colution.

It is only Idea in wich way it work for You system we must study.

Good Luck

In any case it seems that no problem to find fundamental matrix of system so we needed to solve system only in one period (0,tau).

The numerical mesold to keep the periodic is very difficalty(bu using divided diferece on time). I suggest use the spectrum method, that take the solution as a fourier series and find the coifficient numerically.

Perhaps the attached link is of interest here.

http://archimede.mat.ulaval.ca/jplessard/Publications_files/final_floquet_SIADS.pdf

Hi

It's not very hard and all math program(eg.matlab) can solve this. but you can used a approximation method for these equation. I load some paper abut it. Dr Amirfakhrian have some paper abut in. 

For Floquet Theory I'd suggest ODE23 over ODE45. ODE45 is not very reliable as shown in: