Method of Lines for Quasilinear Functional Differential Equations - Kamont, Z.; Czernous, W. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
We give a theorem on the estimation of error for approximate solutions to ordinary functional differential equations. The error is estimated by a solution of an initial problem for a nonlinear functional differential equation. We apply this general result to the investigation of convergence of the numerical method of lines for evolution functional differential equations. The initial boundary-value problems for quasilinear equations are transformed (by means of discretization in spatial variables) into systems of ordinary functional differential equations. Nonlinear estimates of the Perron-type with respect to functional variables for given operators are assumed. Numerical examples are given.