A bound on powers of linear operators, with relevance to numerical stability

DOI10.1016/S0893-9659(01)00091-XzbMath1028.47008WikidataQ127211887 ScholiaQ127211887MaRDI QIDQ1861738

Yanyan Li

Publication date: 10 March 2003

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

zbMATH Keywords

heat equationstability analysisfinite-difference schemeCrank-Nicolson methodpower bounded operatorsnumerical analysisresolvent condition

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items (3)

Modified Douglas splitting methods for reaction-diffusion equations ⋮ Asymptotic analysis of powers of matrices ⋮ Convergence in $\ell_2$ and $\ell_\infty$ Norm of One-Stage AMF-W-Methods for Parabolic Problems

Cites Work

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• On resolvent conditions and stability estimates
• Maximum norm contractivity of discretization schemes for the heat equation
• Resolvent conditions for discretizations of diffusion-convection-reaction equations in several space dimensions
• Maximum norm contractivity in the numerical solution of the one-dimensional heat equation
• A discrete Hille-Yosida-Phillips theorem
• A note about ritt's condition, related resolvent conditions and power bounded operators

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