Contd5 Contd5_r Contd8 Contd8_r Contx1 Contx1_r Contx2 Contx2_r Derkf Derkf_r DerkfInt Dop853 Dop853_r Dopri5 Dopri5_r Doprin Doprin_r Dverk Dverk_r DverkInt Odex Odex2 Odex2_r Odex_r Retard Retard_r Ylag Ylag_r

DerkfInt() Sub DerkfInt ( N As  Long, T As  Double, Y() As  Double, Cont As  LongPtr, Optional Info As  Long  ) Initial value problem of a system of first order ordinary differential equations (5(4)-th order Runge-Kutta-Fehlberg method) (Interpolation for dense output) NOTE - THIS PROGRAM IS DEPRECATED AND WILL BE REMOVED IN THE NEXT VERSION. Purpose This is the support routine which interpolates the solution for dense output when an initial value problem of a system of ordinary differential equations is solved by Derkf (or Derkf_r). For the details of interpolants used here, refer to the reference below. Derkf must be called with setting parameter Mode = 2 to enable dense output. Additional function evaluation for dense output is not required. When returned from Derkf with Info = 2 (Info = 1 for last step) after accepted step, the interpolated solution within latest step interval can be computed by using this routine. Parameters [in] N Number of differential equations. (N >= 1) [in] T T at which the interpolated solution is computed. T must be in the interval of the last step. That is, T1 <= T <= T2 where T1 is the value of T on the previous return from Derkf with Info = 2, and T2 is the value on the last return with Info = 2. [out] Y() Array Y(LY - 1) (LY >= N) Interpolated solution at t. [in] Cont Control information for dense output. Obtained value from option parameter Cont of Derkf. [out] Info (Optional) = 0: Successful exit. = -1: The argument N had an illegal value. (N < 1) = -3: The argument Y() is invalid. Reference W H Enright et al. "Interpolants for Runge-Kutta Formulas" ACM Transactions on Mathematical Software Vol.12, No.3, 1986, pp.193-218 Example Program See example program (2) of Derkf and Derkf_r.