Implicit Difference Methods for Quasilinear Differential Functional Equations on the Haar Pyramid | Zendy

Anna Kępczyńska | Zendy

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Implicit Difference Methods for Quasilinear Differential Functional Equations on the Haar Pyramid

Author(s) -

Anna Kępczyńska

Publication year - 2008

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1352

Subject(s) - mathematics , nonlinear system , pyramid (geometry) , mathematical analysis , variable (mathematics) , stability (learning theory) , differential equation , class (philosophy) , numerical stability , numerical partial differential equations , numerical analysis , computer science , geometry , physics , quantum mechanics , machine learning , artificial intelligence

We present a new class of numerical methods for quasilinear first order partial functional differential equations. The numerical methods are difference schemes which are implicit with respect to the time variable. The existence of approximate solutions is proved by using a theorem on difference inequalities. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. Numerical experiments are presented. Results obtained in this paper can be applied to differential integral problems and to equations with deviated variables.

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