Mathematica Solving a differential system with mathematica 8

[Nesrine]

I need to solve a differential system with mathematica that is presented like this :


eqns = {
X1'[t] ==
A[[1]][[1]] X1[t] + A[[1]][[2]] X2[t] + A[[1]][[3]] X3[t] +
A[[1]][[4]] X4[t] + A[[1]][[5]] X5[t] + A[[1]][[6]] X6[t],
X2'[t] ==
A[[2]][[1]] X1[t] + A[[2]][[2]] X2[t] + A[[2]][[3]] X3[t] +
A[[2]][[4]] X4[t] + A[[2]][[5]] X5[t] + A[[2]][[6]] X6[t],
X3'[t] ==
A[[3]][[1]] X1[t] + A[[3]][[2]] X2[t] + A[[3]][[3]] X3[t] +
A[[3]][[4]] X4[t] + A[[3]][[5]] X5[t] + A[[3]][[6]] X6[t],
X4'[t] ==
A[[4]][[1]] X1[t] + A[[4]][[2]] X2[t] + A[[4]][[3]] X3[t] +
A[[4]][[4]] X4[t] + A[[4]][[5]] X5[t] + A[[4]][[6]] X6[t],
X5'[t] ==
A[[5]][[1]] X1[t] + A[[5]][[2]] X2[t] + A[[5]][[3]] X3[t] +
A[[5]][[4]] X4[t] + A[[5]][[5]] X5[t] + A[[5]][[6]] X6[t],
X6'[t] ==
A[[6]][[1]] X1[t] + A[[6]][[2]] X2[t] + A[[6]][[3]] X3[t] +
A[[6]][[4]] X4[t] + A[[6]][[5]] X5[t] + A[[6]][[6]] X6[t]};


The elements of my matrix A have been already calculated
I used the function NDSolve as follow :

sol = NDSolve[{eqns,
X1[0] == X2[0] == X3[0] == X4[0] == X5[0] ==
X6[0] == {1, 1, 1, 1, 1, 1}}, {X1, X2, X3, X4, X5, X6}, {t, 0,
T}, MaxSteps -> \[Infinity]]

but it only gives me an interpolatingfunction value , or me I need the expression in function of time t of my 6 solutions so that I can use them later for my program.

Can you help me please ??

Thanks a lot

 

[Bill Simpson]

NDSolve is the *Numerical* differential equation solver and is going to give you a *numerical* result. If you need a closed form algebraic solution you are going to need to find a way to coax DSolve into to solve your problem.

 

[Nesrine]

Thanks for your answer I used NDSolve actually and I'm trying to simulate my program with it but I know that I can use Runge Kutta to resolve such problem the thing is that I don't know if there is in mathematica a function that allow me to do a 4th order runge kutta integration

 

[Bill Simpson]

Does this answer your question?

http://reference.wolfram.com/mathematica/tutorial/NDSolvePlugIns.html

"...Classical Runge-Kutta
Here is an example of how to set up and access a simple numerical algorithm.
...
This defines a method function so that NDSolve can obtain the proper difference order to use for the method. The template is used because the difference order for the method is always 4."

Or this

http://reference.wolfram.com/mathematica/tutorial/NDSolveImplicitRungeKutta.html

 

[Nesrine]

Thank you very much Bill I'll try with the reference you gave it to me

I'll keep you posted