Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 1, Pages 57-67
doi:10.1155/S1048953396000068
On the solution of the Liouville equation over a rectangle
1University of York, Department of Mathematics, Heslington, York Y01 5DD, UK
2Department of Electronics, University of York, United Kingdom
Received 1 September 1992; Revised 1 October 1995
Copyright © 1996 A. M. Arthurs et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Methods for integral equations are used to derive pointwise bounds for the
solution of a boundary value problem for the nonlinear Liouville partial differential equation over a rectangle. Several test calculations are performed and the
resulting solutions are more accurate than those obtained previously by other
methods.