The stability of rational approximations of analytic semigroups

DOI10.1007/BF01990345zbMath0783.65050OpenAlexW1971142716WikidataQ59593917 ScholiaQ59593917MaRDI QIDQ2366653

Michel Crouzeix, Stig Larsson, Vidar Thomée, Serguei Piskarev

Publication date: 10 March 1994

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01990345

zbMATH Keywords

Banach spaceanalytic semigroupsCrank-Nicolson methodrational approximations\(A\)-acceptable

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items

Functional calculus estimates for Tadmor-Ritt operators ⋮ FUNCTIONAL CALCULI FOR SECTORIAL OPERATORS AND RELATED FUNCTION THEORY ⋮ Stability of the crank-nicolson scheme and maximal regularity for parabolic equations in spaces ⋮ Contractivity results for alternating direction schemes in Hilbert spaces ⋮ Crank–Nicolson Scheme for Abstract Linear Systems ⋮ ON WELL-POSEDNESS OF DIFFERENCE SCHEMES FOR ABSTRACT PARABOLIC EQUATIONS INL^P([0,T;E) SPACES] ⋮ Error growth analysis via stability regions for discretizations of initial value problems ⋮ Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes ⋮ On the bounds of approximations of holomorphic semigroups ⋮ Discretisation of abstract linear evolution equations of parabolic type ⋮ Unnamed Item ⋮ Computing Semigroups with Error Control ⋮ Numerical Homogenization Methods for Parabolic Monotone Problems ⋮ Decay rate of \(\exp (A^{-1}t)A^{-1}\) on a Hilbert space and the Crank-Nicolson scheme with smooth initial data ⋮ Direct and converse theorems for iterative methods of solving irregular operator equations and finite difference methods for solving ill-posed Cauchy problems ⋮ Stabilizations of the Trotter-Kato theorem and the Chernoff product formula ⋮ On the Crank-Nicolson scheme once again ⋮ Rational approximation schemes for bi-continuous semigroups ⋮ A Besov algebra calculus for generators of operator semigroups and related norm-estimates ⋮ Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions ⋮ Runge-Kutta convolution quadrature methods for well-posed equations with memory ⋮ On the Stability of Variable Stepsize Rational Approximations of Holomorphic Semigroups ⋮ Stability of linear multistep methods for sectorial operators in Banach spaces ⋮ The stability of rational approximations of cosine functions on Hilbert spaces ⋮ On convergence rates in approximation theory for operator semigroups ⋮ Rational inversion of the Laplace transform ⋮ Stabilized approximations of strongly continuous semigroups ⋮ Stability of Rational Multistep Approximations of Holomorphic Semigroups ⋮ From finite differences to finite elements. A short history of numerical analysis of partial differential equations ⋮ Runge-Kutta Approximation of Quasi-Linear Parabolic Equations ⋮ Remarks on the rational approximation of holomorphic semigroups with nonuniform partitions ⋮ Stability results for fractional step discretizations of time dependent coefficient evolutionary problems ⋮ On the approximations of derivatives of integrated semigroups. II ⋮ On positivity, shape, and norm-bound preservation of time-stepping methods for semigroups ⋮ Numerical range and quasi-sectorial contractions ⋮ Resolvent Estimates for Elliptic Finite Element Operators in One Dimension ⋮ \(A\)-stable Runge-Kutta methods for semilinear evolution equations ⋮ A note on the second order of accuracy difference schemes for hyperbolic--parabolic equations ⋮ On variable stepsize Runge-Kutta approximations of a Cauchy problem for the evolution equation ⋮ Higher order Grünwald approximations of fractional derivatives and fractional powers of operators ⋮ Resolvent conditions for discretizations of diffusion-convection-reaction equations in several space dimensions ⋮ On the convergence of rational approximations of semigroups on intermediate spaces ⋮ Stability of Runge-Kutta methods for abstract time-dependent parabolic problems: The Hölder case ⋮ The Upper Bounds for Powers of Linear Operators and Some Applications to the Stability Analysis of Difference Problems ⋮ Numerical ranges and stability estimates ⋮ Optimal orders of convergence for Runge-Kutta methods and linear, initial boundary value problems ⋮ A note about ritt's condition, related resolvent conditions and power bounded operators ⋮ Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems ⋮ Stability in the numerical solution of the heat equation with nonlocal boundary conditions ⋮ Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation

Cites Work

• Unnamed Item
• Unnamed Item
• Semigroups of linear operators and applications to partial differential equations
• On multistep approximation of semigroups in Banach spaces
• Besov spaces and applications to difference methods for initial value problems
• Inverses of Generators
• A Stability Result for Sectorial Operators in Banach Bpaces
• Semidiscretization in Time for Parabolic Problems
• Powers of Generators of Holomorphic Semigroups
• Order stars and stability theorems
• On Rational Approximations of Semigroups
• Stability and Convergence Rates in $L^p$ for Certain Difference Schemes.
• Finite-Element Methods for a Strongly Damped Wave Equation

This page was built for publication: The stability of rational approximations of analytic semigroups