Number: Math 65/93
Author(s): LEPP, Riho.
Title: Discrete approximation of Hammerstein integral equations in the space of essentially bounded functions. 20 p.
Language: English
Keywords: Discrete approximation; integral equations.
ABSTRACT. This paper considers the discretization approach in the
approximate solution of the Hammerstein equation of the form
x(s) = K(s,t)f(t,x(t)) (dt) + y(s), s D R, where the
kernel K and the superposition operator f are supposed to be so
discontinuous that we are forced to look for a solution x in
the space L (D) of essentially bounded functions. For a special
partition of the integration domain D the discrete convergence of
elements is defined in L (D) and the Hammerstein equation
approximated by a sequence of finite dimensional equations.