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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.
`