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

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

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.