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

DOI10.2478/s11533-009-0038-zzbMath1189.65118OpenAlexW2146535622MaRDI QIDQ2268526

Marzenna Pytel-Kudela, Julian Janus, Anatoliy K. Prykarpatsky, Miroslaw Luśtyk

Publication date: 8 March 2010

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-009-0038-z

zbMATH Keywords

convergenceBanach spacesLagrangian interpolationdiscrete approximationnonlinear operator equationsdifferential operator equationsLeray-Schauder type fixed point theoremLie-algebraic representationprojection-algebraic Calogero type methodrealizibility

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solutions to equations with nonlinear operators (65J15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (3)

Generalized pseudospectral method and zeros of orthogonal polynomials ⋮ On completely integrable Calogero-type discretizations of nonlinear Lax integrable dynamical systems and related Markov-type coadjoint orbits ⋮ On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model

Cites Work

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• A Borsuk-Ulam Type Generalization of the Leray-Schauder Fixed Point Theorem
• On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials
• Solution of linear partial differential equations by Lie algebraic methods
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