SDAINI(3)

SYNOPSIS
SUBROUTINE SDAINI (X, Y, YPRIME, NEQ, RES, JAC, H, WT, IDID, RPAR, * IPAR, PHI, DELTA, E, WM, IWM, HMIN, UROUND, NONNEG, NTEMP)

NAME
sdaini - Initialization routine for SDASSL.

LIBRARY
SLATEC (DASSL)

TYPE
SINGLE PRECISION (SDAINI-S, DDAINI-D)

AUTHOR
Petzold, Linda R., (LLNL)

DESCRIPTION
C----------------------------------------------------------------- SDAINI TAKES ONE STEP OF SIZE H OR SMALLER WITH THE BACKWARD EULER METHOD, TO FIND YPRIME. X AND Y ARE UPDATED TO BE CONSISTENT WITH THE NEW STEP. A MODIFIED DAMPED NEWTON ITERATION IS USED TO SOLVE THE CORRECTOR ITERATION. THE INITIAL GUESS FOR YPRIME IS USED IN THE PREDICTION, AND IN FORMING THE ITERATION MATRIX, BUT IS NOT INVOLVED IN THE ERROR TEST. THIS MAY HAVE TROUBLE CONVERGING IF THE INITIAL GUESS IS NO GOOD, OR IF G(X,Y,YPRIME) DEPENDS NONLINEARLY ON YPRIME. THE PARAMETERS REPRESENT: X -- INDEPENDENT VARIABLE Y -- SOLUTION VECTOR AT X YPRIME -- DERIVATIVE OF SOLUTION VECTOR NEQ -- NUMBER OF EQUATIONS H -- STEPSIZE. IMDER MAY USE A STEPSIZE SMALLER THAN H. WT -- VECTOR OF WEIGHTS FOR ERROR CRITERION IDID -- COMPLETION CODE WITH THE FOLLOWING MEANINGS IDID= 1 -- YPRIME WAS FOUND SUCCESSFULLY IDID=-12 -- SDAINI FAILED TO FIND YPRIME RPAR,IPAR -- REAL AND INTEGER PARAMETER ARRAYS THAT ARE NOT ALTERED BY SDAINI PHI -- WORK SPACE FOR SDAINI DELTA,E -- WORK SPACE FOR SDAINI WM,IWM -- REAL AND INTEGER ARRAYS STORING MATRIX INFORMATION C-----------------------------------------------------------------

ROUTINES CALLED
SDAJAC, SDANRM, SDASLV

REVISION HISTORY (YYMMDD)
830315 DATE WRITTEN
901009 Finished conversion to SLATEC 4.0 format (F.N.Fritsch)
901019 Merged changes made by C. Ulrich with SLATEC 4.0 format.
901026 Added explicit declarations for all variables and minor cosmetic changes to prologue. (FNF)
901030 Minor corrections to declarations. (FNF)