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solving odes

From: Piotr
Subject: solving odes
Date: Wed, 15 Jun 2011 13:44:28 +0200
User-agent: Thunderbird (X11/20090105)

Hello. I want to solve numerically the system of ODEs:


$y_n'(t)=y_n(t)a(t)+y_{n-1}(t)b(t)+y_n(t)x(t),  y_n(0)=y_n, n>0,$

where $a, b$ are given functions and $x$ is the solution of the auxiliary problem:

$x'(t)=f(t,x(t)), x(0)=x_0,$

and $n>0$ is some natural number, which can be sometimes huge.

I approximated solution of the auxiliary problem by lsode. Then I interpolated it by a piecewise linear function and solve the main equation for $n=1$ by lsode. For $n=2$ I tried to apply the same procedure with interpolation of $x$ and $y_1,$ but it failed. Could somebody suggest me a better (simpler) approach to this problem? I'm a newbie in Octave, so my idea is not sophisticated. I would be grateful for any help. Piotr.

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