The routines solve the general n-dimensional first-order system,
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_odeiv2_system
datatype.
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 vector elements f_i(t,y,params) in the array dydt, for arguments (t,y) and parameters params. The function should return
GSL_SUCCESS
if the calculation was completed successfully. Any other return value indicates an error. Use return values distinct from standard GSL error codes to distinguish your function as the source of the error.int (* jacobian) (double t, const double y[], double * dfdy, double dfdt[], void * params);
- This function should store the vector of derivative elements df_i(t,y,params)/dt in the array dfdt and the Jacobian matrix J_{ij} in the array dfdy, regarded as a row-ordered matrix
J(i,j) = dfdy[i * dimension + j]
wheredimension
is the dimension of the system. The function should returnGSL_SUCCESS
if the calculation was completed successfully. Any other return value indicates an error. Use return values distinct from standard GSL error codes to distinguish your function as the source of the error.Some of the simpler algorithms do not make use of the Jacobian matrix, so it is not always strictly necessary to provide it (the
jacobian
element of the struct can be replaced by a null pointer for those algorithms). However, it is useful to provide the Jacobian to allow the solver algorithms to be interchanged—the best algorithms make use of the Jacobian.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.