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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 10, pp. 1363–1387, October, 2013.
Deceased (Z. Kamont)
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Czernous, W., Kamont, Z. Method of Lines for Quasilinear Functional Differential Equations. Ukr Math J 65, 1514–1541 (2014). https://doi.org/10.1007/s11253-014-0876-0
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DOI: https://doi.org/10.1007/s11253-014-0876-0