Comparison of explicit and implicit difference methods for quasilinear functional differential equations
We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit and implicit difference methods.
We use a comparison technique with nonlinear estimates of Perron type for given functions with respect to the functional variables.