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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.

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
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