Stability estimates based on numerical ranges with an application to a spectral method

DOI10.1007/BF01955870zbMath0806.65101OpenAlexW2082163527MaRDI QIDQ1334995

Jos L. M. van Dorsselaer, Willem H. Hundsdorfer

Publication date: 1 November 1994

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01955870

zbMATH Keywords

stabilityconvection-diffusion equationmultistep methodsspectral collocation methodtime-stepping method

Mathematics Subject Classification ID

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

Resolvent conditions for discretizations of diffusion-convection-reaction equations in several space dimensions, On the contractivity of implicit-explicit linear multistep methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On resolvent conditions and stability estimates
• Stability radius of polynomials occurring in the numerical solution of initial value problems
• A generalization of the numerical range of a matrix
• Matrix valued versions of a result of von Neumann with an application to time discretization
• Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues
• Stability of the Chebyshev collocation approximation to the advection- diffusion equation
• The CFL Condition for Spectral Approximations to Hyperbolic Initial-Boundary Value Problems
• On the Use of Stability Regions in the Numerical Analysis of Initial Value Problems
• The Stability of Pseudospectral-Chebyshev Methods