Estimates of variable stepsize Runge-Kutta methods for sectorial evolution equations with nonsmooth data

DOI10.1016/S0168-9274(01)00126-XzbMath1005.65056OpenAlexW2018544796MaRDI QIDQ1612427

Barnabas M. Garay, Wolf-Jürgen Beyn

Publication date: 22 August 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(01)00126-x

zbMATH Keywords

stabilityerror boundsinitial value problemBanach spaceRunge-Kutta methodsnonsmooth datavariable stepsizesemilinear evolution equationssectorial operator equations

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solutions to equations with nonlinear operators (65J15) Error bounds for numerical methods for ordinary differential equations (65L70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (6)

On the stability of parabolic differential and difference equations with a time-nonlocal condition ⋮ The stability of difference schemes of second-order of accuracy for hyperbolic-parabolic equations ⋮ Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions ⋮ A note on the second order of accuracy difference schemes for hyperbolic--parabolic equations ⋮ Stability of difference schemes for hyperbolic-parabolic equations ⋮ Estimates of variable stepsize Runge-Kutta methods for sectorial evolution equations with nonsmooth data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On resolvent conditions and stability estimates
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• On variable stepsize Runge-Kutta approximations of a Cauchy problem for the evolution equation
• A second order backward difference method with variable steps for a parabolic problem
• Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization
• Some problems of well-posedness of difference schemes on non-uniform grids
• \(A(\Theta)\)-stable approximation of abstract Cauchy problems
• Analysis of discretizations of parabolic problems in pairs of spaces
• Estimates of variable stepsize Runge-Kutta methods for sectorial evolution equations with nonsmooth data
• On well-posedness of the nonlocal boundary value problem for parabolic difference equations
• Interior estimates for time discretizations of parabolic equations
• On the bounds of approximations of holomorphic semigroups
• On the Discretization in Time of Semilinear Parabolic Equations with Nonsmooth Initial Data
• Error Estimates for Spatially Discrete Approximations of Semilinear Parabolic Equations with Nonsmooth Initial Data
• Upper Semicontinuity of Attractors for Approximations of Semigroups and Partial Differential Equations
• Single step methods for inhomogeneous linear differential equations in Banach space
• On Rational Approximations of Semigroups
• On the Stability of Variable Stepsize Rational Approximations of Holomorphic Semigroups
• Runge-Kutta Methods for Parabolic Equations and Convolution Quadrature
• Stability of Time-Stepping Methods for Abstract Time-Dependent Parabolic Problems
• Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
• Fractional powers of operators
• Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour

This page was built for publication: Estimates of variable stepsize Runge-Kutta methods for sectorial evolution equations with nonsmooth data