Numerical methods for nonlinear first-order partial differential equations with deviated variables

Abstract

In the article classical solutions of initial problems for nonlinear differential equations with deviated variables are approximated by solutions of quasilinear systems of difference equations. Interpolating operators on the Haar pyramid are used. 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. This new approach to solving nonlinear equations with deviated variables numerically is based on a method of linearization for initial problems. Numerical examples are given. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005