<DOC>
<DOCNO>
1087
</DOCNO>
<TITLE>
convergence rates of iterative treatments of partial differential equations
.
</TITLE>
<AUTHOR>
frankel, s.p.
</AUTHOR>
<BIBLIO>
math. tables aids comp. v. 4. p. 65, 1950 .
</BIBLIO>
<TEXT>
the development of high-speed digital computers has made feasible the
numerical solution by iterative methods of some partial differential
equations . the convergence rates of several such iterative methods are
estimated here . it is found that with the familiar elementary iterative
 methods some quite simple problems require prohibitive computational
labor .
the iterative methods here considered are related to the various forms
of the southwell /relaxation method/ in that they involve successively
applied local corrections to improve an approximate solution . however,
these iterative methods are routinized in conformity with the requirements
of automatic computers while the relaxation method is flexible and
 depends in an essential way on the skill of its practitioners .
</TEXT>
</DOC>
