On the solution of the Liouville equation over a rectangle. (English) Zbl 0855.35041
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.
Reviewer: Michael Sever (Jerusalem)
MSC:
35J65 | Nonlinear boundary value problems for linear elliptic equations |
45P05 | Integral operators |
65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |