[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## [Help-gsl] Boundary value problem for system of ODEs

**From**: |
Ruben Farinelli |

**Subject**: |
[Help-gsl] Boundary value problem for system of ODEs |

**Date**: |
Thu, 23 Apr 2015 00:30:07 +0200 |

Hi,
I have been working for a long time on a complicate physical problem.
I have a set of ODEs, three of which are first-order, and the fourth
is of second order.
In the latter case unfortunately, I have conditons for its derivative
R'[0]=0,
while the second is actually an asymptotic boundary condition, namely
the function must tend to zero for large value of the variable.
Of course with a change of variable the system becomes N+1
first order ODEs.
Actually I have implemented some kind of shooting method, the main
issue is that the function has an exponential-decay behavior and
the result seems to be rather dependent on the adopted integrator.
Finally I decided to compute the complicate Jacobian to test
the gsl_odeiv_bsimp which I read should be the most powerful.
A-part from any welcome suggestion in approaching BVPs, I have
a doubt. Namely, the right-hand side of the system contains not only
the functions y_i but also their first derivatives, labeled F_i, or y'_i.
I mean something like
F[0]=f_0{y[0]...y[n], F[1].....F[n]}
F[1]=f_1{y[0]...y[n], F[0].....F[n]}
etc etc
The GSL jacobian function arguments are
(double t, const double y[], double *dfdy, double dtdy[], void *params)
but I don't see where the functions derivative y'_i are stored.
They are still present when computing the Jacobian, but apparently
they are not read.
Is there something wrong ?
Thank you for your help !
Ruben

**[Help-gsl] Boundary value problem for system of ODEs**,
*Ruben Farinelli* **<=**