State. and ZIP Code) ... Technical Report. PRO.M ... B. Neta. Naval Postgraduate School. Department of Mathematics. Code MA ...... Florida State University.
VPS-MA-91-009
NAVA POSTGRADUATE SCHOOL Monterey, California AD-A235 489
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SOFTWARE FOR THE PARALLEL SOLUTION OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
Levi Lustman Beny Neta
February 1991 Approved for public release; distribution unlimited Prepared for: Naval Postgraduate School Monterey, CA 93943
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Software for the Parallel Solution of Systems of Ordinary Differential Equations 12 PiRSONAL AUTHOR(S)
Levi Lustman and Beny Neta 0a1 TYPE OP REPORT 16 SUPPLEMENIARY
17 FIELD
114
13l.b TIME COVERED
Technical Report
PRO.M1/291
. 2/25/91j
DATE OF REPORT lye r. on?i. Day)
15 PAGE COUNT
28 February 191
28
NOTATION
(OSAII COOES SUB-GROUP
18 SUBJECTF If MS
IGROUP
lContinue on reverse if necessary and
idenity
by block
numbev)
ordinary differential equations, parallel processing, hypercube
19 ABs (RACI (Continue on reverse ifnecessary and identity by block number)
This report contains software for the solution of systems of ordinary differential
*equations on an INTEL iPSC/2 hypercube. from the second author.
A diskette is available upon request
20
OISIMUTION IAVAILAILITY OF ABSTRACT 1K3INsCtASSIFIIco1NLMITED SAME AS jja IIAME OF II(SPUNSIIILE INDIVIDUAL
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Levi Lustman and Beny Neta DU FORM 1473.814 MAR
21. ABSTRACT SECURITY CLASSIFICATION
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I 83 APR edition may be used untlexhausted All other edition%are obsoletteUCASFE
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SECURITY CIASSIFICATION Or THIS PAGE
Software for the Parallel Solution of Systems of Ordinary Differential Equations
L. Lustman B. Neta
Naval Postgraduate School Department of Mathematics Code MA Monterey, CA 93943
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Abstract This report contains software for the solution of systems of ordinary differential equations on an INTEL iPSC/2 hypercube. A diskette is available upon request from the second author.
, ma=a mar ~ m m mmmm
m
1
1.
Introduction
In this report we supply software for the numerical solution of systems of ordinary differential equations (ODEs) on an INTEL iPSC/2 hypercube. The first program can only be used to solve linear initial or boundary value systems of ODEs and based on an algorithm developed by Katti and Neta (1989) and improved by Lustman et al (1990). The second program is based on polynomial extrapolation and Gragg's scheme and is useful for nonlinear ODEs as well. This algorithm is described in Lustman, Neta and Gragg (1991).
2
2.
Linear Systems
In this section we give the software for the solution of linear systems of ODEs: y'(x) = Ay(x) +g(x), a < x < b y(a) = y The algorithm used was developed by Katti and Neta (1989) and improved by Lustman et al (1990). The host and node program are given. The subroutines sa, sf and putex give the matrix A, the right hand side of (1) and the exact solution (for debugging purposes) respectively. An example of input and output corresponding to these subroutines are attached.
3
C C
HOST c c solving initial value problems by multiple shooting c on INTEL iPSC/2 hypercube having 8 (maxnp) processors C
c
see
Lustman, Neta & Katti
C
" change everywhere, in both node and host programs, ndim=3 c c to whatever value is appropriate. C
program mshivph integer intype, inlen, outype, out len integer ymtype, ymlength integer n ,np,ndim,nin,nout, m , mnp integer allnodes, hostpid, nodepid parameter (nmax=lOO) parameter (ndim=3, nout~1) parameter (maxnp=8) parameter (nin=nmax*maxnp+ndim+lO) parameter (intype=lO,outype=20, inlen=4*nin # ymtype=30,ymlength=ndim* (ndim+l) *4 # outlen=4*nout,allnodes= -1 # hostpid=8, nodepid=14) common/cmn/n, ndimc, ninc, noutc #,m,mp,h, left,right,g,x real g (ndim) , x (O:nmax*maxnp) , yin (1) real vout (flout) , left , right equivalence # (n,vin(l)),(ndimc,vin(2)),(ninc,vin(3)) # ' (noutc,vin(4)) ,(m,vin(5)), (mp,vin(6)) #1 (h,vin(7)), (left,vin(8)), (right,vin(9)) #: (g (1) , vin(10) ) #, (x(O) ,vin(lO+ndim)) ndimc=ndim ninc=nin noutc=nout '61 call getcube('shoot',' call setpid (hostpid) print*,' got the maximal cube,',numnodeso,' nodes' call load( 'node' ,allnodes,nodepid) print*,' after load' print*,' enter ',ndim,' initial values g' read*, (g(i) ,i=l,ndim) print*,' enter endpoints of interval' read*, left, right print*,'solve for ',left,,
