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

Ylag_r() Sub Ylag_r ( I As  Long, T As  Double, RCont() As  Double, ICont() As  Long, YY As  Double, IRev As  Long  ) Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) (Reverse communication version) (Interpolation for back-values of solution) NOTE - THIS PROGRAM IS DEPRECATED AND WILL BE REMOVED IN THE NEXT VERSION. Purpose This routine is the support routine which computes the back-values of the solution by interpolation for solving an initial value problem of the delay differential equations and dense output by Retard_r. Parameters [in] I Element number of solution to be interpolated. (0 <= I <= N - 1) [in] T T at which the interpolated solution is computed. T must be in the interval of the available back steps. Otherwise. 0 will be returned and Retard_r will be terminated with Info = 14. The number of back steps available through this routine depends on the allocated working memory, and it is determined by the size of RCont() (LRCont) when Retard_r is called. [in] RCont() Array RCont(LRCont - 1) (LRCont >= Mxst*(5*Nrdens) Control information for back-values of the solution. Enter RCont() used for Retard_r without change. [in] ICont() Array ICont(LICont - 1) (LICont >= Nrdens) Control information for back-values of the solution. Enter ICont() used for Retard_r without change. [in,out] YY [in] IRev = 1: Enter the value of Y(I) at T in YY and call this routine again (note that t0 - τ <= T <= t0). This is same with Phi in the case of Ylag so that the function value at up to τ before t0 must is defined. For the components which do not need retarded argument in the definition of differential equations, IRev = 1 will not be returned. [out] IRev = 0: Interpolated solution Y(I) at T. [in,out] IRev Control variable for reverse communication. [in] Before first call, IRev should be initialized to zero. On succeeding calls, IRev should not be altered. [out] If IRev is not zero, complete the following tasks and call this routine again without changing IRev. = 0: Computation finished. = 1: The value of Y(I) at T must be given in YY. Reference E. Hairer, S.P. Norsett and G. Wanner, "Solving Ordinary Differential Equations. Nonstiff Problems. 2nd edition", Springer Series in Computational Mathematics, Springer-Verlag (1993) Example Program Compute y(t - τ). where I is the component number (0 to N - 1) and T is t - τ. RCont() and ICont() must be passed without altering those values. The result is returned in YY when IRev = 0. If t0 - τ <= T <= t0 (where t0 is the initial value of t), IRev = 1 is returned. Then the value of Y(I) at T must be given in YY. IRev = 0 Do Call Ylag_r(I, T, RCont(), ICont(), YY, IRev) If IRev = 1 Then YY = value of Y(I) at T (where t0 - τ <= T <= t0) Loop While IRev <> 0