Contd5 Contd5_r Contd8 Contd8_r Contx1 Contx1_r Contx2 Contx2_r Deabm Deabm_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) 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.