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READING4.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME READING4
* Problem :
* *********
* A nonlinear optimal control problem from Nancy Nichols
* with a given initial condition.
* This problem arises in tide modelling.
* Source: a variant upon a problem in
* S. Lyle and N.K. Nichols,
* "Numerical Methods for Optimal Control Problems with State Constraints",
* Numerical Analysis Report 8/91, Dept of Mathematics,
* University of Reading, UK.
* SIF input: Ph. Toint, Aug 1992
* classification OOR2-MN-V-V
* Number of discretized points in [0,1] (n = N+1, m = N )
*IE N 2 $-PARAMETER n=3, m=2 original value
*IE N 50 $-PARAMETER n=51, m=50
*IE N 100 $-PARAMETER n=101, m=100
*IE N 500 $-PARAMETER n=501, m=500
*IE N 1000 $-PARAMETER n=1001, m=1000
IE N 5000 $-PARAMETER n=5001, m=5000
* Mesh
IA N-1 N -1
RI RN N
RD H RN 1.0
RM 2/H RN 2.0
RM H/2 H 0.5
RM 1/H RN 1.0
RM -1/H RN -1.0
* Constants
RE PI 3.141592653589
RM 2PI PI 2.0
RE A 0.07716
RD 1/A A 1.0
RM 1/2A 1/A 0.5
RM 2A A 2.0
R* H/2A H 1/2A
RD 2A/H H/2A 1.0
* Constants
IE 0 0
IE 1 1
IE 2 2
VARIABLES
X X(0)
DO I 1 N
X X(I)
ND
GROUPS
ZN J 'SCALE' 1/A
DO I 1 N
ZG U(I)
ND
RANGES
DO I 1 N
X READING4 U(I) 1.0
ND
BOUNDS
XX READING4 X(0) 0.25
DO I 1 N
XL READING4 X(I) -0.5
XU READING4 X(I) 0.5
ND
ELEMENT TYPE
EV UC X
EV UC XP
EP UC T
EV ENERGY X
EV ENERGY XP
EP ENERGY T
ELEMENT USES
DO I 1 N
RI RI I
R* TI RI H
IA I-1 I -1
XT I(I) ENERGY
ZV I(I) X X(I)
ZV I(I) XP X(I-1)
ZP I(I) T TI
XT UC(I) UC
ZV UC(I) X X(I)
ZV UC(I) XP X(I-1)
ZP UC(I) T TI
ND
GROUP USES
XE J I(1) -1.0
DO I 2 N-1
XE J I(I) -2.0
ND
XE J I(N) -1.0
DO I 1 N
ZE U(I) UC(I) 2A/H
ND
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
ELEMENTS READING4
* Least-square groups
TEMPORARIES
R F
R C
R D
M COS
INDIVIDUALS
T ENERGY
A F COS(2.0*3.141592653589*T)
F ( F - X ) * ( X - XP )
G X - 2.0 * X + XP + F
G XP - ( F - X )
H X X -2.0
H X XP 1.0
T UC
A F COS(2.0*3.141592653589*T)
A C ( X - XP ) / ( F - X )
A D ( 1.0 + C ) / ( F - X )
F C
G X D
G XP - 1.0 / ( F - X )
H X X 2.0 * D / ( F - X )
H X XP -1.0 / ( F - X )**2
ENDATA