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READING9.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME READING9
* 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: Nick Gould and Ph. Toint, March 1995
* classification OOR2-MN-V-V
* Number of discretized points in [0,1] - 1
*IE N+1 3 $-PARAMETER n=6, m=2
*IE N+1 51 $-PARAMETER n=102, m=50
*IE N+1 101 $-PARAMETER n=202, m=100
*IE N+1 201 $-PARAMETER n=402, m=200
*IE N+1 501 $-PARAMETER n=1002, m=500 original value
*IE N+1 1001 $-PARAMETER n=2002, m=1000
IE N+1 5001 $-PARAMETER n=10002, m= 5000
* Mesh
IA N N+1 -1
IA N-1 N -1
RI RN N
RD H RN 1.0
RM -H/2 H -0.5
* Constants
RE K1 0.07716
RE K2 0.07716
R* K1H K1 H
RA K1H+1 K1H 1.0
RM -K1H-1 K1H+1 -1.0
R* K2H K2 H
* Constants
IE 0 0
IE 1 1
IE 2 2
VARIABLES
DO I 0 N
X P(I)
ND
DO I 0 N
X U(I)
ND
GROUPS
ZN OBJ
DO I 0 N-1
IA I+1 I 1
XE S(I) P(I+1) 1.0
ZE S(I) P(I) -K1H-1
ND
CONSTANTS
DO I 0 N-1
RI RI I
R* T RI H
R( SINT SIN T
R* HSINT H SINT
Z READING9 S(I) HSINT
ND
BOUNDS
DO I 0 N
XU READING9 U(I) 1.0
XR READING9 P(I)
ND
XX READING9 P(0) 0.0
START POINT
V READING9 'DEFAULT' 0.2
ELEMENT TYPE
EV PROD U
EV PROD P
EV PROD2 U
EV PROD2 P
ELEMENT USES
DO I 0 N
XT OE(I) PROD2
ZV OE(I) P P(I)
ZV OE(I) U U(I)
ND
DO I 0 N-1
XT CE(I) PROD
ZV CE(I) P P(I)
ZV CE(I) U U(I)
ND
GROUP USES
DO I 0 N-1
IA I+1 I 1
ZE OBJ OE(I) -H/2
ZE OBJ OE(I+1) -H/2
ZE S(I) CE(I) K2H
ND
OBJECT BOUND
* Solution
*XL SOLUTION -4.41677D-02 $ (n=500)
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
ELEMENTS READING9
INDIVIDUALS
T PROD
F U * P
G U P
G P U
H U P 1.0
T PROD2
F ( U * P ) ** 2
G U 2.0 * U * P ** 2
G P 2.0 * P * U ** 2
H U U 2.0 * P ** 2
H U P 4.0 * U * P
H P P 2.0 * U ** 2
ENDATA