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ODE System with Variable Coefficients

  1. Oct 27, 2011 #1
    hi
    suppose we have this equation :

    d/dt(X)=A(t)*X



    x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients.
    coefficients of equations and consequently A are depend on t which is time.

    how i Solve this equation ?

    thanks
     
  2. jcsd
  3. Oct 28, 2011 #2

    lurflurf

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  4. Oct 28, 2011 #3
    hi
    in this article that explain the method of peani baker

    http://arxiv.org/pdf/1011.1775v1

    i can not understand how in page 5 for first example it calculate element (1,2) of I(t)(with subscript n)

    can anybody help?
     
    Last edited: Oct 28, 2011
  5. Oct 28, 2011 #4

    lurflurf

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    by induction
    [In(t)](1,2)=∫([A(t)](1,1)[In-1(t)](1,2)+[A(t)](1,2)[In-1(t)](2,2))dt
    =∫((1)(tn-1αn-1/(n-1)!)+(t)((a t)n-1/(n-1)!))dt
    and so on
     
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