Numerical approximations of parabolic functional differential equations on unbounded domains

The paper is concerned with initial problems for nonlinear parabolic functional differential equations. A general class of difference methods is constructed. A theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type with an unknown function of several variables is presented. The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that given function satisfy nonlinear estimates of the Perron type with respect to a functional variable. Results obtained in the paper can be applied to differential integral problems and equations with retarded variables. Numerical examples are presented.