deabm deabm_r derkfa derkfa_r dop853a dop853a_r dopn1210 dopn1210_r dopn43 dopn43_r dopn64 dopn64_r dopn86 dopn86_r dopri5a dopri5a_r dverka dverka_r odex2a odex2a_r odexa odexa_r retarda retarda_r ylaga

ylaga() void ylaga ( int  i, int  n, double  t, double  y[], void(*)(int, int, double, double *, int *)  phi, double  work[], int  iwork[], int *  info  ) Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) (Computation of back-values of solution) Purpose This program is the support program which computes the back-values of the solution by interpolation for solving an initial value problem of the delay differential equations by Retard. A system of first order delay ordinary differential equations of the form dy/dt = f(t, y(t), y(t - τ), y(t - τ2), ...), y = y0 at t = t0 where f depends on the values at previous points y(t - τ), y(t - τ2), .... These values can be computed by using this program. This program is the rewrite of YLAG used for the 5(4)-th order Dormand-Prince code for delay equations, RETARD (Reference (1)). Parameters [in] i Element number of y to be interpolated. (1 <= i <= n or i = 0) 1 <= i <= n: Only the i-th element of y is computed. i = 0: All elements of y (y[0] 〜 y[n - 1]) are computed. [in] n Number of differential equations. (n >= 1) [in] t Independent variable. To compute back-value y(t - τ), for example, t - τ is given to this argument. [out] y[] Array y[ly] (ly >= 1 (1 <= i <= n), ly >= n (i = 0)) The values of dependent variable at t (interpolation of numerical solution). 1 <= i <= n: The computed i-th element of y is returned in y[0]. i = 0: All computed elements are returned in y[0] 〜 y[n - 1]. [in] phi The user supplied subroutine, which returns the values of y at t < t0, defined as follows. void phi(int i, int n, double t, double y[], int *info) { y[] = values of y at t (where t0 - τ < t < t0); *info = 0; } If i = 0, all elements must be stored in y[0] 〜 y[n - 1]. Otherwise, i-th element must be stored in y[0]. Only the values of i, which are used in ylaga by the user, may be supported. ylaga will terminate if phi returns info != 0. [in] work[] Array work[*] Control information. work[] which is used for retarda or retarda_r must be passed without change. [in] iwork[] Array iwork[*] Integer control information. iwork[] which is used for retarda or retarda_r must be passed without change. [out] info Return code. = 0: Successful exit. < 0: The (-info)-th argument is invalid. = 11: (Error) Invalid control information. = 12: (Error) t is too small. iwork[6] of retarda may be too small. = 13: (Error) t is too large. = Others: phi returnd this value (!= 0) as info. Reference (1) E. Hairer, S.P. Norsett and G. Wanner, "Solving Ordinary Differential Equations. Nonstiff Problems. 2nd edition", Springer Series in Computational Mathematics, Springer-Verlag (1993)