ESAIM: Mathematical Modelling and Numerical Analysis

Table of Contents - January 2007 - Volume 41, Issue 01  

Research Article

On the rate of convergence of a collocation projection of the KdV equation

Kalisch, Henrika1 and Raynaud, Xaviera2

a1 Department of Mathematics, University of Bergen, 5008 Bergen, Norway. henrik.kalisch@mi.uib.no

a2 Department of Mathematics, NTNU, 7491 Trondheim, Norway. raynaud@math.ntnu.no

Abstract

Based on estimates for the KdV equation in analytic Gevrey classes, a spectral collocation approximation of the KdV equation is proved to converge exponentially fast.

(Received March 31 2006)

(Revised July 11 2006)

(Online publication April 26 2007)

Key Words:

  • Spectral methods;
  • convergence rate;
  • collocation projection;
  • analytic Gevrey class.

Mathematics Subject Classification:

  • 35Q53;
  • 65M12;
  • 65M70