Stiffness 1952--2012: sixty years in search of a definition

DOI10.1007/s10543-014-0503-3zbMath1317.65154OpenAlexW2111917268MaRDI QIDQ2350726

Laurent O. Jay, Gustaf Söderlind, Manuel Calvo

Publication date: 25 June 2015

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-014-0503-3

zbMATH Keywords

stabilitynumerical exampleinitial value problemsresearch surveystiffnessstep sizelogarithmic normsstiffness factorreference time scalestiffness indicatorvan der Pol and Oregonator equation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical methods for stiff equations (65L04)

Related Items (10)

Blendstrings: an environment for computing with smooth functions ⋮ A note on approximate Jacobians of implicit Runge-Kutta methods and convergence of modified Newton iterations ⋮ Variable stepsize multivalue collocation methods ⋮ An Hermite-Obreschkoff method for stiff high-index DAE ⋮ Multivalue collocation methods free from order reduction ⋮ Computation and Applications of Mathieu Functions: A Historical Perspective ⋮ A family of \(L\)-stable singly implicit peer methods for solving stiff IVPs ⋮ A Lyapunov and Sacker-Sell spectral stability theory for one-step methods ⋮ Variations on a Theme of Euler ⋮ Optimal residuals and the Dahlquist test problem

Uses Software

• RODAS
• deTestSet

Cites Work

• Stiffness of ODEs
• Stiff ODE solvers: A review of current and coming attractions
• Stiffness in numerical initial-value problems
• The logarithmic norm. History and modern theory
• Fifty Years of Stiffness
• Stiffness detection and estimation of dominant spectrum with explicit Runge-Kutta methods
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Review Paper: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations
• Digital filters in adaptive time-stepping
• Integration of Stiff Equations
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