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.



Paper:
Available as PDF (360 Kbytes), Postscript (1368 Kbytes) or gzipped PostScript (464 Kbytes; uncompress using gunzip).
Author(s):
Helge Holden, <holden@math.ntnu.no>
Xavier Raynaud, <raynaud@math.ntnu.no>
Publishing information:
Comments:
Submitted by:
<holden@math.ntnu.no> July 22 2004.


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