AN ERROR ANALYSIS OF THE DISCRETE GALERKIN SCHEME FOR NONLINEAR INTEGRAL EQUATIONS

  • YOUNG-HEE KIM (Department of Mathematics Yonsei University) ;
  • MAN-SUK SONG (Department of Computer Science Yonsei University)
  • Published : 1994.04.01

Abstract

We employ the Galerkin method to solve the nonlinear Urysohn integral equation (1.1) x(t) = f(t) + $∫_{D}$ k(t, s, x(s))ds (t $\in$ D), where D is a bounded domain in $R^{d}$ , the function f and k are known and x is the solution to be determined. We assume that D has a locally Lipschitz boundary ([1, p. 67]). We can rewrite (1.1) in operator notation as x = f + Kx. We consider (1.1) as an operator equation on $L_{\infty$}$(D) and assume that K is defined on the closure $\Omega$ of a bounded open set $\Omega$$L_{\infty}$(D). Throughout our analysis we put the following assumptions on (1.1).(omitted)(1.1).(omitted)

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