ODE System with Variable Coefficients

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Discussion Overview

The discussion revolves around solving a system of ordinary differential equations (ODEs) with variable coefficients, specifically represented as d/dt(X) = A(t)*X, where X is a column matrix and A(t) is a matrix of coefficients dependent on time. The scope includes methods for solving such equations, particularly focusing on the Peano-Baker method and its application.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant inquires about solving the ODE system with variable coefficients.
  • Another participant suggests using the Peano-Baker method as a solution technique.
  • A third participant references an article explaining the Peano-Baker method and expresses confusion regarding a specific calculation in the article.
  • A later reply proposes a formula involving induction to calculate a specific element of the matrix I(t), detailing the integral form based on previous elements.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the solution method, as there are varying levels of understanding and application of the Peano-Baker method, along with specific calculations that remain unclear to some.

Contextual Notes

There are limitations in understanding the application of the Peano-Baker method, particularly regarding the specific calculations and assumptions made in the referenced article. The discussion does not resolve these uncertainties.

yashar
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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
 
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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:
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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