d01asf

Purpose

Synopsis

[result,abserr,lst,erlst,rslst,ierlst,iw,ifail] = d01asf(g,a,omega,epsabs<,...
key,limlst,liw,ifail>)

Description

 
 D01ASF is an adaptive routine, designed to integrate a function
 of the form g(x)w(x) over a semi-infinite interval, where w(x) is
 either sin((omega)x) or cos((omega)x). Over successive intervals
 
                 C =[a+(k-1)c,a+kc],   k=1,2,...,LST
                  k                           
 
 integration is performed by the same algorithm as is used by 
 D01ANF. The intervals C  are of constant length
                        k                 
 
           c={2[|(omega)|]+1}(pi)/|(omega)|,  (omega)/=0
 
 where [|(omega)|] represents the largest integer less than or 
 equal to |(omega)|. 
 
 If (omega)=0 and KEY = 1, the routine uses the same algorithm as 
 D01AMF (with EPSREL = 0.0).
 
 In contrast to the other routines in Chapter D01, D01ASF works 
 only with a user-specified absolute error tolerance (EPSABS). 
 Over the interval C  it attempts to satisfy the absolute accuracy
                    k                                     
 requirement
                          EPSA =U *EPSABS
                              k  k 
                k-1                         
 where U =(1-p)p   , for k=1,2,... and p=0.9.
        k                                   
 
 However, when difficulties occur during the integration over the 
 kth sub-interval C  such that the error flag IERLST(k) is non-
                   k                                      
 zero, the accuracy requirement over subsequent intervals is 
 relaxed. 
 

Parameters

d01asf

Required Input Arguments:

g                                     function (User-Supplied)
a                                     real
omega                                 real
epsabs                                real

Optional Input Arguments:                       <Default>

key                                   integer  2
limlst                                integer  50
liw                                   integer  1000
ifail                                 integer  -1

Output Arguments:

result                                real
abserr                                real
lst                                   integer
erlst (limlst)                        real
rslst (limlst)                        real
ierlst (limlst)                       integer
iw (liw)                              integer
ifail                                 integer