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## solving odes

 From: Piotr Subject: solving odes Date: Wed, 15 Jun 2011 13:44:28 +0200 User-agent: Thunderbird 2.0.0.19 (X11/20090105)

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

\$y_0(t)=some\_given\_function,\$

\$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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