Generalized Euler method for nonlinear first order partial differential equations - Kamont, Z.; Newlin-Łukowicz, J. (Нелінійні коливання, 2003)
Classical solutions of nonlinear first order partial differential equations are approximated in the paper by solutions of quasilinear systems of difference equations. Sufficient conditions for the convergence of the method are given. The proof of the stability of the difference problem is based on a comparison method. Nonlinear estimates of the Perron type are assumed for increment functions. This new approach to a numerical solving of nonlinear equations is generated by a method of quasilinearization for mixed problems. Numerical examples are given