The jet of derivatives

Its prototype is

MY_FLOAT **taylor_coefficients_ODE_NAME(MY_FLOAT t,
                                        MY_FLOAT *x,
                                        int order);

taylor_coefficients_ODE_NAME returns a static two dimensional arrary. The rows are the Taylor coefficients of the state variables.

Parameters

• t: value of the time variable. It is used only when the system of ODEs is nonautonomous.
• x: value of the state variables.
• order: degree of Taylor polynomial.

If you want to compute several jets at the same point but with increasing orders, then you should consider using the call

MY_FLOAT **taylor_coefficients_ODE_NAMEA(MY_FLOAT t,
                                         MY_FLOAT *x,
                                         int order,
                                         int rflag)

(note the ``A'' at the end of the name). The first three parameters have the same meaning as before, and the meaning of the fourth one is:

0: the jet is computed from order 1 to order order.

1: the jet is computed starting from the final order of the last call, up to order.

Care must be exercised if you invoke this routine with rflag=1. If you modify the Taylor coefficients and/or the base point, you need to restore them before the next call.

The algorithm used to generate the Taylor coefficients is described in Appendix A.