| Author(s): G.A. Erskine and K.S. Kölbig | Library: MATHLIB |
| Submitter: | Submitted: 07.06.1992 |
| Language: Fortran | Revised: |
Subroutine subprograms RFRDH1, DFRDH1 and function subprograms RFRDH2, DFRDH2 calculate an approximation to the solution y of the Fredholm integral equation
over the interval [a,b]. The function F must not be identically zero.
The interval [a,b] may be divided into m subintervals
, with
.
The order 
(number of abscissae) of the Gaussian quadrature
formula used for integrating over 
is specified
separately for each subinterval.
Function subprograms RFRDH3 and DFRDH3 evaluate numerically
integrals of the form 
where H is an arbitrary function and y is the solution of (1).
The following values of 
may be used:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
20, 24, 32, 40, 48, 64, 80, 96.
On computers other than CDC and Cray, only the double-precision versions DFRDH1 etc. are available. On CDC and Cray computers, only the single-precision versions RFRDH1 etc. are available.
Structure:
SUBROUTINE and FUNCTION subprograms
User Entry Names: RFRDH1, RFRDH2, RFRDH3,
DFRDH1, DFRDH2, DFRDH3
Files Referenced: Unit 6
External References: 
Usage:
For 
(type REAL), 
(type
DOUBLE PRECISION), the first step in the solution of (1)
must be the execution of a statement of the form:
CALL tFRDH1(F,G,M,T,NG,WS,IDIM,N)
,
subprogram G must set 
.
of subintervals in [a,b].
. On entry,
T must contain the m+1 ordered points of subdivision
, with 
and 
.
. On entry, NG must contain the order
(number of absissae) 
of the Gaussian quadrature formula to be used
in the interval 
.
. Used as working space and for
communication between the subprograms.
.
.
Once tFRDH1 has been called, the function subprograms tFRDH2 and tFRDH3 may be referenced any number of times without any further call to tFRDH1.
In any arithmetic expression,
tFRDH2(F,G,X,WS,IDIM,N)has the value
, where y is the approximate solution of
(1).
In any arithmetic expression,
tFRDH3(H,WS,IDIM,N)has the approximate value of
where y is the approximate solution of (1).
H (type according to t) is the name of a user-defined
FUNCTION subprogram, declared EXTERNAL in the calling
program. This subprogram must set
.
Method:
Let the sets 
and 
be defined by
and 
are respectively the weights and
abscissae of the 
-point Gaussian quadrature formulae corresponding
to the interval 
.
Subprograms RFRDH1 or DFRDH1 sets up and solves the following
system of
simultaneous linear equations with unknowns 
:
where 
.
Function subprogram tFRDH2 calculates
.
Function subprogram tFRDH3 calculates
.
Accuracy:
The accuracy depends upon the extend to which the product G(x,t)y(t)
can be represented by a polynomial of degree 
for all x in the
interval 
.
Error handling:
Error D601.1: In tFRDH1, the system of
linear equations is singular. A message is written on Unit 6,
unless subroutine MTLSET (N002) has been called.
If any of the values 
does not appear in the list given above,
a message is written on Unit 6 by RGSET or DGSET
(D107) unless subroutine MTLSET (N002) has been called.
