24.1 Defining the ODE System

The routines solve the general n-dimensional first-order system,

dy_i(t)/dt = f_i(t, y_1(t), ..., y_n(t))

for i = 1, \dots, n. The stepping functions rely on the vector of derivatives f_i and the Jacobian matrix, J_{ij} = df_i(t,y(t)) / dy_j. A system of equations is defined using the gsl_odeiv_system datatype.

Data Type: gsl_odeiv_system

This data type defines a general ODE system with arbitrary parameters.

int (* function) (double t, const double y[], double dydt[], void * params)

This function should store the elements of f(t,y,params) in the array dydt, for arguments (t,y) and parameters params

int (* jacobian) (double t, const double y[], double * dfdy, double dfdt[], void * params);

This function should store the elements of f(t,y,params) in the array dfdt and the Jacobian matrix J_{ij} in the the array dfdy regarded as a row-ordered matrix J(i,j) = dfdy[i * dim + j] where dim is the dimension of the system.

size_t dimension;

This is the dimension of the system of equations

void * params

This is a pointer to the arbitrary parameters of the system.