Preprint 2004-038

Convergence of a finite difference scheme for the Camassa–Holm equation

Helge Holden and Xavier Raynaud

Abstract: We prove that a certain finite difference scheme converges to the weak solution of the Cauchy problem on a finite interval with periodic boundary conditions for the Camassa–Holm equation ut-uxxt+3uux -2uxuxx-uuxxx=0 with initial data u|t=0=u0H1([0,1]). Here it is assumed that u-u0''≥0 and in this case, the solution is unique, globally defined, and energy preserving.

Available as PDF (360 Kbytes), Postscript (1368 Kbytes) or gzipped PostScript (464 Kbytes; uncompress using gunzip).
Helge Holden, <>
Xavier Raynaud, <>
Publishing information:
Submitted by:
<> July 22 2004.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
2004-07-22 13:07:16 UTC