W. Czernous
abstract:
We present a new class of numerical methods for nonlinear first order partial
differential equations. Classical solutions of mixed problems are approximated
in the paper by solutions of suitable quasilinear systems of difference
equations. We give a complete convergence analysis for the methods and we show
by an example that the new methods are considerably better than the classical
schemes. The proof of the stability is based on a comparison technique with
nonlinear estimates of the Perron type.
Mathematics Subject Classification: 35R10, 65M12
Key words and phrases: Initial boundary value problems, stability and convergence, nonlinear estimates of the Perron type, bicharacteristics