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## Re: [Help-gsl] Solving a First Order ODE system using GSL

**From**: |
Warren Weckesser |

**Subject**: |
Re: [Help-gsl] Solving a First Order ODE system using GSL |

**Date**: |
Tue, 10 Nov 2009 21:59:40 -0600 |

You can treat your equation as a system that happens to have just one
dimension, and implement it the same way you would an n-dimensional system.
I have attached code that solves the Solow equation (from economics); it is
basically the same as the example in the reference manual, but modified for
this first order equation. The jacobian is just the derivative of the
right-hand side of the equation with respect to the dependent variable (x,
in your case; k, for the Solow model).
Warren
On Tue, Nov 10, 2009 at 12:09 PM, Earl, Joseph <address@hidden
>* wrote:*
>* Hi,*
>
>* I am trying to solve a first-order ODE of the form*
>
>* x' = sqrt(1/3x - k + lx^2)*
>
>* using the GSL C++ library, where k and l are constants for a particular*
>* solution.*
>
>* I have no problem at all using GSL to solve 2nd order (such as x'' = -x)*
>* and higher ODEs, something is just confusing about the first order equations*
>* and how to put them into the required form.*
>* The Jacobian doesn't seem to make much sense with a 1st order ODE.*
>
>* Also the current documentation is pretty poor - there is only one example*
>* of a 2nd order ODE which is repeated all over the net. So if anyone wants to*
>* add a 1st order example to the help docs I'm sure that would be of some use*
>* to others (and me!) in the future.*
>
>* Any help would be much appreciated (if you feel like writing out a full*
>* working example that would be awesome).*
>
>* Regards,*
>* Joseph Earl*
>* Imperial College London*
>
>* _______________________________________________*
>* Help-gsl mailing list*
>* address@hidden*
>* http://lists.gnu.org/mailman/listinfo/help-gsl*
>

**
**`gsl_1d_ode.c`

*Description:* Binary data