CALLING DDAPLUS

The code DDAPLUS is normally called via Athena Visual Studio. For very detailed control of the available options, DDAPLUS may be called as follows from a user-provided MAIN program for the given problem  

CALL DDAPLUS(t,tout,Nstvar,U,UPRIME,Rtol,Atol,Info, 

A Rwork,Lrw,lwork,Liw,Rpar,lpar,ldid,LUI IREP,LUNERR,lrange, 

B lmodel,laux,fsub,Esub,Jac,Bsub,lpass,Filepath,Lenpath) 

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MAIN For each problem Driver calls DDAPLUS... 

The initial UPRIME and h are ready at t = to, along with U updated from to- whenever algebraic equations are present. This is the normal return when DDAPLUS is called with tout=t. To commence integration, MAIN must call DDAPLUS again with tout moved from t in the direction indicated by the sign of h in Rwork(3). 

The code has taken about Iwork(21) steps (counted as Iwork(ll) — Iwork(lO)) on this call. If you want to continue, set Info(l)=l in MAIN and call DDAPLUS again another Iwork(21) steps will be allowed. 

This subroutine calculates the nonzero elements of df/du, for use by DDAPLUS in computing G t to) or G(to) for systems with dE/du = 0. Jac is executed only if MAIN sets lnfo(5) to 1 before calling DDAPLUS. 

The derivatives F r are called the first-order parametric sensitivities of the model. Their direct computation via Newton s method is implemented in Subroutines DDAPLUS (Appendix B) and PDAPLUS. Finite-difference approximations are also provided as options in GREGPLUS to produce the matrix A in either the Gauss-Newton or the full Newton form these approximations are treated in Problems 6.B and 6.C. 

In this section we describe the arguments used in calls to DDAPLUS. 

Set lnfo(l)=0 to indicate that this is an initial call of DDAPLUS, or the start of a new region with changed equations, with to reset to the current t. 

This integer, when positive, is called lYstop and indicates that the state or sensitivity variable U(IYstop) must not cross the value Cstop in the current integration. If the index Info(17) is outside the set of variables indicated in Info(15), DDAPLUS will write a diagnostic message and return control to the calling program. 

The main task of DDAPLUS is to compute the state vector u (and the sensitivity matrix W if requested) at the next output point. The status of the solution upon return to the calling program is described by the parameter Idid, whose possible values are explained below. 

Control is being returned to the calling program because Ires (see description in subroutine fsub) has been set to —2. You cannot continue the integration when this condition occurs. An explanation will appear in the output if the value Ires=-2 was set by a module of DDAPLUS if not, rerun the problem after inserting WRITE statements in your subroutines to explain whenever one of them sets Ires to —2. 

The argument Ires is zero on entry, and should not be altered unless the current call of Jac is unsuccessful. In the latter event, set Ires to a negative value before return DDAPLUS will then set Ires=—2 and... 

After each successful call of Jac, DDAPLUS completes the iteration matrix G in Pdwork with the following formulas, which follow from Eqs. (B.l-5a) and (B.l-5b) when dE/du is zero ... 

When Info(12)>0 and Info(14) = l, Bsub will be called by DDAPLUS, and may be organized as in the following pseudocode. 

The following Athena Visual Studio code solves this test example by calls to DDAPLUS and tabulates the four state variables as functions of time. 

The following Athena Visual Studio code sets up this problem and solves it by calls to DDAPLUS. The chosen absolute tolerance, ATOL=l.D-10, is satisfactory until f = 1.00 hr, after which ui and g attain much smaller values. Careful nesting of the multiplications and divisions proved necessary to avoid underflows in the calculations of /g, fg, and fig note the placement of parentheses in those lines of the UModel Equations section. 

The following Athena Visual Studio code sets up this problem and solves it by call to DDAPLUS. The Athena nomenclature for the state and sensitivity functions is given by the following ... 

Here, as in Example C.3, the subroutine MODEL contains IF blocks to access the equations and parameters for the current reaction model. DDAPLUS is called to solve the current model for its expectation values Fi tu, 0) and (when IDER.EQ.l) its parametric sensitivities dFi[tu- 6)/d6j. 

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