Crank–Nicolson Scheme for Abstract Linear Systems

DOI10.1080/01630560701380981zbMath1151.65048OpenAlexW2170799336MaRDI QIDQ5297957

Serguei Piskarev, Hans J. Zwart

Publication date: 16 July 2007

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630560701380981

zbMATH Keywords

Crank-Nicolson schemeCayley transforminfinite-dimensional system\(C_{0}\)-semigroup

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Numerical solutions to equations with linear operators (65J10) Linear differential equations in abstract spaces (34G10) Finite difference and finite volume methods for ordinary differential equations (65L12) Applications of functional analysis to differential and integral equations (46N20) Applications of functional analysis in numerical analysis (46N40)

Related Items (8)

The perturbation algorithm for the realization of a four-layer semi-discrete solution scheme of an abstract evolutionary problem ⋮ Abstract degenerate Volterra integro-differential equations: inverse generator problem ⋮ Decay rate of \(\exp (A^{-1}t)A^{-1}\) on a Hilbert space and the Crank-Nicolson scheme with smooth initial data ⋮ On the Crank-Nicolson scheme once again ⋮ On the perturbation algorithm for the semidiscrete scheme for the evolution equation and estimation of the approximate solution error using semigroups ⋮ On the approximations of derivatives of integrated semigroups. II ⋮ The Cayley transform of the generator of a polynomially stable \(C_0\)-semigroup ⋮ Inverses of generators of integrated fractional resolvent operator functions

Cites Work

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• Well-posedness of delay parabolic difference equations
• The stability of rational approximations of analytic semigroups
• On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform
• A Stability Result for Sectorial Operators in Banach Bpaces
• POWER-BOUNDED OPERATORS AND RELATED NORM ESTIMATES

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