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Infinite systems of first order PFDEs with mixed conditions

100%
Czernous W.
Annales Polonici Mathematici
|
2008
|
tom 94
|
nr 3
209-230
EN
We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems can be derived from the general model by specializing the operators.
2
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Generalized method of lines for first order partial functional differential equations

100%
Czernous W.
Annales Polonici Mathematici
|
2006
|
tom 89
|
nr 2
103-126
EN
Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization in time of the method of lines considered in this paper leads to new difference schemes for the original problem. It is shown by examples that the new method is considerably better than the classical schemes.
3
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Comparison of explicit and implicit difference methods for quasilinear functional differential equations

63%
Czernous W., Kamont Z.
Applicationes Mathematicae
|
2011
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tom 38
|
nr 3
315-340
EN
We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit and implicit difference methods. We use a comparison technique with nonlinear estimates of Perron type for given functions with respect to the functional variables.:wn
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