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CHANDHEQ.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CHANDHEQ
* Problem :
* *********
* Chandrasekhar Radiative Transfer H equation, as stated by T. Kelley.
* Source: problem 4 in
* J.J. More',
* "A collection of nonlinear model problems"
* Proceedings of the AMS-SIAM Summer seminar on the Computational
* Solution of Nonlinear Systems of Equations, Colorado, 1988.
* Argonne National Laboratory MCS-P60-0289, 1989.
* SIF input: Ph. Toint, Dec 1989.
* classification NOR2-RN-V-V
* N is the number of discretization points
*IE N 10 $-PARAMETER original value
*IE N 50 $-PARAMETER
IE N 100 $-PARAMETER
* The value of the problem parameter C should be in [0,1] for a
* physically realistic problem, but other values can be used for
* testing purposes.
* Unique solution for C=0 and C=1, two for other values.
* More difficult for C close to 1.
RE C 1.0 $-PARAMETER in [0,1]
* Define useful parameters
IE 1 1
RE 1.0 1.0
RI RN N
R/ 1/N 1.0 RN
RM HALFC C 0.5
* Discretization points (X(I)) and weights (W(I)) for the considered
* quadrature rule on [0,1]
DO I 1 N
RI RI I
A* X(I) RI 1/N
AA W(I) 1/N 0.0
ND
VARIABLES
DO I 1 N
X H(I)
ND
GROUPS
DO I 1 N
XE G(I) H(I) 1.0
ND
CONSTANTS
X CHANDHEQ 'DEFAULT' 1.0
BOUNDS
* Positive variables
START POINT
V CHANDHEQ 'DEFAULT' 1.0
ELEMENT TYPE
EV 2PR HI HJ
ELEMENT USES
T 'DEFAULT' 2PR
DO I 1 N
DO J 1 N
ZV A(I,J) HI H(I)
ZV A(I,J) HJ H(J)
ND
GROUP USES
DO I 1 N
A* T1 HALFC X(I)
DO J 1 N
A* T3 T1 W(J)
A+ XIPXJ X(I) X(J)
R/ VAL T3 XIPXJ
RM COEFF VAL -1.0
ZE G(I) A(I,J) COEFF
ND
OBJECT BOUND
LO CHANDHEQ 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CHANDHEQ
INDIVIDUALS
T 2PR
F HI * HJ
G HI HJ
G HJ HI
H HI HJ 1.0
ENDATA