Method of Lines for Quasilinear Functional Differential Equations
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 10, pp 1514-1541.
Citation Example: Czernous W., Kamont Z. Method of Lines for Quasilinear Functional Differential Equations // Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1363–1387.