Difference functional inequalities and applications
Abstract. The paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
Keywords: initial boundary value problems, difference functional inequalities, difference methods, stability and convergence, interpolating operators, error estimates.
Mathematics Subject Classification: 35R10, 65M12, 65M15.