Extrapolation of Nystrom Solution for Two-Dimensional Nonlinear Fredholm Integral Equations

  • Authors:

  • Han Guoqiang;Wang Jiong

  • Affiliations:

  • Department of Mathematical Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. han@simplex.t.u-tokyo.ac.jp&semi/ hayami@simplex.t.u-tokyo.ac.j ...;Department of Computer and Electronic Engineering, Guangdong Provincial Institute for Technical Person, Guangzhou, Guangdong Province, People's Republic of China

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 1999

Quantified Score

Hi-index 0.01

Visualization

Abstract

In this paper, we analyze the existence of asymptotic error expansion of Nystrom solution for two-dimensional nonlinear Fredholm integral of the second kind. We show that the Nystrom solution admits an error expansion in powers of the step-size h and the step-size k. For a special choice of the numerical quadrature, the leading terms in the error expansion for the Nystrom solution contain only even powers of h and k, beginning with terms h2p and k2q. These expansions are useful for the application of Richardson extrapolation and for obtaining sharper error bounds. Numerical examples show that how Richardson extrapolation gives a remarkable increase of precision, in addition to faster convergence.