Numerical method of lines for evolution functional differential equations

Abstract We give a theorem on error estimates of approximate solutions for the ordinary functional differential equation. The error is estimated by a solution of an initial problem for nonlinear differential functional equation. We apply this general result to the investigation of the convergence of the numerical method of lines generated by evolution functional differential equations. Initial boundary value problems for Hamilton Jacobi functional differential equations and parabolic functional differential problems are considered. Nonlinear estimates of the Perron type with respect to the functional variable for given operators are assumed.