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FLETCBV2.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME FLETCBV2
* Problem :
* *********
* Another Boundary Value problem.
* Source: The first problem given by
* R. Fletcher,
* "An optimal positive definite update for sparse Hessian matrices"
* Numerical Analysis report NA/145, University of Dundee, 1992.
* but assuming that the 1/h**2 term should read h**2
* This is what Fletcher intended (private communication).
* The author comments: "The problem arises from discretizing the bvp
* x"=-2+sin x in [0,1]
* with x(0)=0, x(1)=1. This gives a symmetric system of equations,
* the residual vector of which is the gradient of the given function."
* He multiplies through by h^2 before integrating.
* SIF input: Nick Gould, Nov 1992.
* classification OUR2-AN-V-0
* The number of variables is N.
*IE N 10 $-PARAMETER original value
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 5000 $-PARAMETER
*IE N 10000 $-PARAMETER
* KAPPA a parameter.
RE KAPPA 1.0 $-PARAMETER
*RE KAPPA 0.0 $-PARAMETER
* Define useful parameters
IE 0 0
IE 1 1
IE 2 2
RE 1.0 1.0
IA N-1 N -1
IA N+1 N 1
RI RN+1 N+1
R/ H 1.0 RN+1
R* H2 H H
R* KAPPAH2 H2 KAPPA
RM -KAPPAH2 KAPPAH2 -1.0
RM -2H2 H2 -2.0
RA -1-2H2 -2H2 -1.0
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
XN G(0) X(1) 1.0
DO I 1 N-1
IA I+1 I 1
XN G(I) X(I) 1.0 X(I+1) -1.0
ND
XN G(N) X(N) 1.0
DO I 1 N-1
ZN L(I) X(I) -2H2
ND
ZN L(N) X(N) -1-2H2
DO I 1 N
ZN C(I)
ND
BOUNDS
FR FLETCBV2 'DEFAULT'
START POINT
DO I 1 N
RI RI I
R* IH RI H
Z FLETCBV2 X(I) IH
ND
ELEMENT TYPE
EV COS V
ELEMENT USES
T 'DEFAULT' COS
DO I 1 N
ZV C(I) V X(I)
ND
GROUP TYPE
GV HALFL2 GVAR
GROUP USES
DO I 0 N
XT G(I) HALFL2
ND
DO I 1 N
ZE C(I) C(I) -KAPPAH2
ND
OBJECT BOUND
* Solution
*LO SOLTN ??
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS FLETCBV2
TEMPORARIES
M COS
M SIN
INDIVIDUALS
T COS
F COS( V )
G V - SIN( V )
H V V - COS( V )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS FLETCBV2
INDIVIDUALS
T HALFL2
F 5.0D-1 * GVAR * GVAR
G GVAR
H 1.0D+0
ENDATA