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Help! Complex-valued ODEs and the "jac" function in GSL ODE solver?
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Help! Complex-valued ODEs and the "jac" function in GSL ODE solver? |
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Sun, 3 Jun 2007 01:11:34 -0700 |
Help! Complex-valued ODEs and the "jac" function in GSL ODE solver?
Hi all,
I am new to GSL ode, I started looking it because I really need to speed my
current Matlab program, which runs ODE solvers repeatedly for thousands to
millions of times. I found the GSL example ode program difficult to
understand, and here are my questions:
(1)
I have to solve the following complex-valued non-linear ODE numerically,
using GSL's ode solver. But it seems that GSL's ode solver only supports
real-valued ODE...
My ODEs are:
y' = c1 * y + c2 + c3*exp(c4* y + c5*i)
x' = c6 * y
here c1, c2, c3, c4, c5 and c6 are real numbers , and "i" is the unit of
imaginary numbers.
I am planning to decompose y into yr and yi, x into xr and xi, the real
parts and the imaginary parts. And solve separately:
yr' = c1 * yr + c2 + c3*exp(c4* yr)*cos(c4* yi + c5)
yi' = c1 * yi + c2 + c3*exp(c4* yr)*sin(c4* yi + c5)
xr' = c6 * yr
xi' = c6 * yi
--------------------
Am I right? Is this the best approach to handle the ODEs with a solver only
supports real values?
My original solutions were already too slow, now by having to solve 4
equations, it is even slower, and double the computing time...
Any better approaches?
(2)
In the sample GSL ode code, there is a function called "jac", how do I
define the "jac" function for my ODE equations, as shown above?
int
jac (double t, const double y[], double *dfdy,
double dfdt[], void *params)
{
double mu = *(double *)params;
gsl_matrix_view dfdy_mat
= gsl_matrix_view_array (dfdy, 2, 2);
gsl_matrix * m = &dfdy_mat.matrix;
gsl_matrix_set (m, 0, 0, 0.0);
gsl_matrix_set (m, 0, 1, 1.0);
gsl_matrix_set (m, 1, 0, -2.0*mu*y[0]*y[1] - 1.0);
gsl_matrix_set (m, 1, 1, -mu*(y[0]*y[0] - 1.0));
dfdt[0] = 0.0;
dfdt[1] = 0.0;
return GSL_SUCCESS;
}
---------------------
There is no documentation talking about this "jac" function. I really don't
know how to define my "jac" function for my own ode equations.
Could you please help me?
Thanks a lot!
Mike
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