rkdp85_dense_coefficients Module Procedure

module procedure rkdp85_dense_coefficients pure module subroutine rkdp85_dense_coefficients(me, b, form) Interface →

Dense output for the Dormand-Prince 8(5) method rkdp85. This is the 7th order continuous extension from DOP853. It requires 4 additional function evaluations (see rkdp85_dense_extra_stages).

The coefficients are given here in the form used in DOP853:

$x(t + \theta h) = r_0 + \theta(r_1 + \theta_1(r_2 + \theta(r_3 + \theta_1(r_4 + \theta(r_5 + \theta_1(r_6 + \theta r_7))))))$, where $\theta_1 = 1 - \theta$

where $r_0 = x(t)$ and $r_j = h \sum_i b_{ij} f_i$.

References

• E. Hairer, S. P. Norsett, G. Wanner, "Solving Ordinary Differential Equations I: Nonstiff Problems", 2nd ed., Springer, 1993.
• DOP853

Arguments

Type	Intent	Optional	Attributes		Name
class(rkdp85_class),	intent(in)			::	me
real(kind=wp),	intent(out),		dimension(:,:), allocatable	::	b	dense output coefficients
integer,	intent(out)			::	form	the form of b