A note on convergence concepts for stiff problems
Copyright policy )A note on convergence concepts for stiff problems
Most convergence concepts for discretizations of nonlinear stiff initial value problems are based on one-sided Lipschitz continuity. Therefore only those stiff problems that admit moderately sized one-sided Lipschitz constants are covered in a satisfactory way by the respective theory. In the present note we show that the assumption of moderately sized one- sided Lipschitz constants is violated for many stiff problems. We recall some convergence results that are not based on one-sided Lipschitz constants; the concept of singular perturbations is one of the key issues. Numerical experience with stiff problems that are not covered by available convergence results is reported.
- TU Wien Austria
numerical examples, convergence, Multiple scale methods for ordinary differential equations, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, stiff differential equations, one- sided Lipschitz continuity, Singular perturbations for ordinary differential equations, logarithmic norms, singular perturbations, Stability and convergence of numerical methods for ordinary differential equations, stiff problems
numerical examples, convergence, Multiple scale methods for ordinary differential equations, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, stiff differential equations, one- sided Lipschitz continuity, Singular perturbations for ordinary differential equations, logarithmic norms, singular perturbations, Stability and convergence of numerical methods for ordinary differential equations, stiff problems
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