The controversial stability analysis

DOI10.1016/S0096-3003(03)00274-1zbMath1032.65103OpenAlexW1970012262MaRDI QIDQ1412491

Ercília Sousa

Publication date: 25 November 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(03)00274-1

zbMATH Keywords

convergencehistorical surveyFinite difference methodStability analysisConvection-diffusion equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for second-order parabolic equations (35K15) History of numerical analysis (65-03)

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Cites Work

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• Note on the von Neumann stability of the explicit FTCS convective diffusion equation
• Vorticity boundary condition and related isssues for finite difference schemes
• Heuristic stability theory for finite-difference equations
• The stability of explicit Euler time-integration for certain finite difference approximations of the multi-dimensional advection-diffusion equation
• The cell Reynolds number myth
• Analysis of error growth for explicit difference schemes in conduction-convection problems
• Stability of finite difference approximations to a diffusion-convection equation
• Analysis of explicit difference methods for a diffusion‐convection equation
• Stability analysis of explicit finite difference schemes for the Navier-Stokes equations
• On the Partial Difference Equations of Mathematical Physics
• A general finite-difference formulation with application to Navier-Stokes equations

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