Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 1, Pages 57-67

On the solution of the Liouville equation over a rectangle

A. M. Arthurs,1 J. Clegg,1,2 and A. K. Nagar1

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.


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.