How to consult GSL ODE with many parameters and harmonic functions - c

Question

I'm working on non-linear differential equation using GSL. The thing is I'm quite new on C stuffs. I just adapted the sample on GNU site into the equation I'm interested in right now.
This is the equation:
d2x/dt2 + r*dx/dy + cos(x) + v*cos(2*x+0.4) E1*sin(wt) + E2*sin(2*w*t+a) = 0
What I am stuck is I have no idea how to plug in multiple parameters in the codes. Moreover, I don't know how to employ cosine or sine function in this code.
I tried to figure out this problem, by searching on Google all the way. I couldn't find any thing that helps me.
#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_odeiv2.h>
int func (double t, const double x[], double y[], void *params)
{
double r = *(double *)params;
double v = *(double *)params;
double w = *(double *)params;
double E1 = *(double *)params;
double E2 = *(double *)params;
double a = *(double *)params;
y[0] = x[1];
y[1] = -r*x[1] - cos(x[0]) - v*cos(2*x[0]+0.4) - E1*sin(w*t) - E2*sin(2*w*t+a);
return GSL_SUCCESS;
}
int jac (double t, const double x[], double *dydx, double dydt[], void *params)
{
double r = *(double *)params;
double v = *(double *)params;
double w = *(double *)params;
double E1 = *(double *)params;
double E2 = *(double *)params;
double a = *(double *)params;
gsl_matrix_view dydx_mat = gsl_matrix_view_array (dydx, 2, 2);
gsl_matrix * m = &dydx_mat.matrix;
gsl_matrix_set (m, 0, 0, 0.0);
gsl_matrix_set (m, 0, 1, 1.0);
gsl_matrix_set (m, 1, 0, sin(x[0]) + 2*v*sin(2*x[0]+0.4));
gsl_matrix_set (m, 1, 1, -r);
dydt[0] = 0.0;
dydt[1] = 0.0;
return GSL_SUCCESS;
}
int main (void)
{
double r = 0.0;
double v = 0.0;
double w = 2.4;
double E1 = -2.3;
double E2 = 0;
double a = 0.7;
gsl_odeiv2_system sys = {func, jac, 2, &r, &v, &w, &E1, &E2, &a};
gsl_odeiv2_driver *d = gsl_odeiv2_driver_alloc_x_new (&sys, gsl_odeiv2_step_rk8pd, 1e-6, 1e-6, 0.0);
int i;
double t = 0.0, t1 = 10000;
double x[2] = {0.0, 0.0};
for (i = 1 ; i<=10000; i++)
{
double ti = i*t1/10000;
int status = gsl_odeiv2_driver_apply (d, &t, ti, x);
if (status != GSL_SUCCESS)
{
printf("error, return value%d\n", status);
break;
}
printf("%.5e %.5e %.5e\n", t, x[0], x[1]);
}
gsl_odeiv2_driver_free (d);
return 0;
}

Answer 1

The params argument is a pointer (address / memory location) to some arbitrary data structure. In the example from the GSL documentation, their equation contained only one parameter, which means it's okay to just pass the address of a double-precision number.
However, for your problem, you need to access 6 different parameters. You can't access every parameter with the same address!
/* this doesn't work! */
double r = *(double *)params;
double v = *(double *)params;
double w = *(double *)params;
double E1 = *(double *)params;
double E2 = *(double *)params;
double a = *(double *)params;
Since all the addresses are the same, you are referring to the same number. To remedy this, you can either: store all the parameters in an array of length 6, or store them in a predefined data structure. The latter approach is more readable so I will demonstrate that.
First define a data type to specify what parameters you will store:
struct param_type {
double r;
double v;
double w;
double E1;
double E2;
double a;
};
Now, create a structure of this type in the main function and store the actual values of the parameter:
struct param_type my_params = {r, v, w, E1, E2, a};
When defining the system, you store a pointer to that struct param_type:
gsl_odeiv2_system sys = {func, jac, 2, &my_params};
To use the parameter inside func and jac, you simply cast the params argument from a generic pointer (void *) to a pointer for your specific data type (struct param_type *):
struct param_type *my_params_pointer = params;
(Note that in C++ this must be written with an explicit cast.) Finally, you can access the parameters via:
double r = my_params_pointer->r;
double v = my_params_pointer->v;
double w = my_params_pointer->w;
double E1 = my_params_pointer->E1;
double E2 = my_params_pointer->E2;
double a = my_params_pointer->a;
The arrow -> is used here instead of the dot . because my_params_pointer is a pointer and needs to be dereferenced before use.

Answer 2

If you are working with parameters, most likely they are of the same type (double). In that case this can be solved too using an array and then access the elements from func and/or jac.
Another option could be use a gsl_vector and then "get" the values inside the functions. This will involve use free.