On positivity, shape, and norm-bound preservation of time-stepping methods for semigroups

DOI10.1016/j.jmaa.2004.09.069zbMath1068.47050OpenAlexW2142641722WikidataQ60580311 ScholiaQ60580311MaRDI QIDQ1772288

Mihály Kovács

Publication date: 18 April 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.09.069

zbMATH Keywords

\(C_0\)-semigroupsfunctional calculustime discretization methods

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Functional calculus for linear operators (47A60)

Related Items (11)

Multivariate approximation by modified Gauss-Weierstrass operators ⋮ Operator splitting for non-autonomous evolution equations ⋮ Rational approximation schemes for bi-continuous semigroups ⋮ On shape preserving semigroups ⋮ Runge-Kutta convolution quadrature methods for well-posed equations with memory ⋮ Rational inversion of the Laplace transform ⋮ Stabilized approximations of strongly continuous semigroups ⋮ Positivity of exponential Runge-Kutta methods ⋮ Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator ⋮ Numerical analysis view on the general Trotter–Kato product formulae ⋮ On the convergence of rational approximations of semigroups on intermediate spaces

Uses Software

• RODAS

Cites Work

• One-parameter semigroups of positive operators
• Maximum norm contractivity of discretization schemes for the heat equation
• Shape preserving properties of some positive linear operators on unbounded intervals
• Preserving concavity in initial-boundary value problems of parabolic type and in its numerical solution
• Contractivity in the numerical solution of initial value problems
• Functional calculi for linear operators in vector-valued \(L^p\)-spaces via the transference principle
• The stability of rational approximations of analytic semigroups
• A Stability Result for Sectorial Operators in Banach Bpaces
• Long-term stability of variable stepsize approximations of semigroups
• Survey of the stability of linear finite difference equations
• High-Accuracy Stable Difference Schemes for Well-Posed Initial-Value Problems
• Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques
• On Rational Approximations of Semigroups
• What is the Laplace Transform?
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