The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

• Autorzy: Miroslaw Lustyk , Julian Janus , Marzenna Pytel-Kudela , Anatoliy Prykarpatsky
• Języki publikacji: EN

Abstrakty

EN

The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated solution sets, based on a Leray-Schauder type fixed point theorem, are obtained.

Słowa kluczowe

EN

Projection-algebraic Calogero type method; Discrete approximation; Lagrangian interpolation; Lie-algebraic representation; Leray-Schauder type fixed point theorem; Convergence; Realizibility

Kategorie tematyczne

• 65N12: Stability and convergence of numerical methods
• 65L07: Numerical investigation of stability of solutions
• 65M12: Stability and convergence of numerical methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 775-786

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Miroslaw Lustyk

• The AGH University of Science and Technology, Krakow, Poland

autor

Julian Janus

• The AGH University of Science and Technology, Krakow, Poland

autor

Marzenna Pytel-Kudela

• The AGH University of Science and Technology, Krakow, Poland

autor

Anatoliy Prykarpatsky

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0038-z