Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
 

Summary: JOURNAL OF INTEGRAL
EQUATIONS AND APPLICATIONS
Volume 1, Number 1, Winter 1988
THE DISCRETE GALERKIN METHOD FOR
NONLINEAR INTEGRAL EQUATIONS (*)
KENDALL ATKINSON AND FLORIAN POTRĄ
ABSTRACT. Let K be a completely continuous nonlinear
integral operator, and consider solving x = K(x) by Galerkin's
method. This can be written as xn = PnK(xn),Pn an or-
thogonal projection; the iterated Galerkin solution is defined
by xn = K(xn). We give a general framework and error anal-
ysis for the numerical method that results from replacing all
integrals in Galerkin's method with numerical integrals. A
special high order formula is given for integral equations aris-
ing from solving nonlinear two-point boundary value prob-
lems.
1. Introduction. Consider the problem of solving the nonlinear
Urysohn integral equation
(1.1) x(i)= I K{t,s,x(s))ds, ted.
Jn

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences