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Method of lines for quasilinear functional differential equations. (English) Zbl 1310.65110

Ukr. Math. J. 65, No. 10, 1514-1541 (2014) and Ukr. Mat. Zh. 65, No. 10, 1363-1387 (2013).
Summary: 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.

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35R10 Partial functional-differential equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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References:

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