ODE System with Variable Coefficients

  • Thread starter yashar
  • Start date
  • #1
31
0
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
 

Answers and Replies

  • #3
31
0
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:
  • #4
lurflurf
Homework Helper
2,440
138
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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