Stiffness of ODEs
Copyright policy )Stiffness of ODEs
This article investigates the performance of (explicit) one-step methods applied to stiff linear differential equations. The effects of ``freezing'' the coefficients and of diagonalizing the matrix is studied. By a series of interesting numerical experiments, it is shown that the scalar test equation \(y' = \lambda y\) does not correctly explain the behaviour of the method when the matrix of the system is highly non- normal. Evidence is given that the numerical integration of a system is in general better controlled by the pseudospectrum of the matrix than by its spectrum.
- Cornell University United States
- University of Strathclyde United Kingdom
- University of Dundee United Kingdom
Multiple scale methods for ordinary differential equations, pseudospectrum, Nonlinear ordinary differential equations and systems, stability, Numerical methods for initial value problems involving ordinary differential equations, 510, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, stiff linear differential equations, one-step methods, numerical experiments, Stability and convergence of numerical methods for ordinary differential equations, Mathematics, performance
Multiple scale methods for ordinary differential equations, pseudospectrum, Nonlinear ordinary differential equations and systems, stability, Numerical methods for initial value problems involving ordinary differential equations, 510, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, stiff linear differential equations, one-step methods, numerical experiments, Stability and convergence of numerical methods for ordinary differential equations, Mathematics, performance
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).67 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!