Numerical methods for hyperbolic functional differential problems on the Haar pyramid
The main topic of the paper is the numerical solution of the Cauchy problem for a system of nonlinear hyperbolic functional differential equations. The authors propose a wide introduction to orient the reader within the literature on this topic. Next they construct a general class of difference methods and prove a theorem on their convergence. Then in the two subsequent sections the authors define interpolating operators on the Haar pyramid, use nonlinear estimates of the Perron type for given functions with respect to the functional variable to obtain results on the error estimate for approximate solutions and apply functional difference inequalities for the stability result. Numerical examples are reported ad the end of the paper.
system of nonlinear hyperbolic functional differential equations
scientific article; zbMATH DE number 1523190