Next: Stepping Functions, Up: Ordinary Differential Equations [Index]
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_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. A
special return value GSL_EBADFUNC
causes gsl_odeiv2
routines to immediately stop and return. The user must call an
appropriate reset function (e.g. gsl_odeiv2_driver_reset
or
gsl_odeiv2_step_reset
) before continuing. 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
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]
where dimension
is the dimension of the system.
Not all of the stepper algorithms of gsl_odeiv2
make use of the
Jacobian matrix, so it may not be necessary to provide this function
(the jacobian
element of the struct can be replaced by a null
pointer for those algorithms).
The function should return GSL_SUCCESS
if the calculation was
completed successfully. Any other return value indicates an error. A
special return value GSL_EBADFUNC
causes gsl_odeiv2
routines to immediately stop and return. The user must call an
appropriate reset function (e.g. gsl_odeiv2_driver_reset
or
gsl_odeiv2_step_reset
) before continuing. Use return values
distinct from standard GSL error codes to distinguish your function as
the source of the error.
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.
Next: Stepping Functions, Up: Ordinary Differential Equations [Index]