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Stiffness in numerical initial-value problems: \(A\) and \(L\)-stability of numerical methods. (English) Zbl 1007.65053
Summary: The main aim of this note is to help students to gain an insight into the asymptotic stability concept by means of visual representation of the stability regions of different numerical methods. This facilitates understanding of the meaning of stability for constant step sizes and the related concept of stiffness in numerical initial-value problems. Moreover, the distinction between \(A\) and \(L\)-stability of numerical methods can be more easily understood.
MSC:
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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