## Modern convergence theory for stiff initial-value problems.(English)Zbl 0782.65087

This is a brief review on theoretical results about convergence of discretization schemes when applied to stiff ordinary differential equations. The authors consider problems satisfying a one-sided Lipschitz-condition and also singular perturbation problems. They mention that the results on $$B$$-convergence extend to problems of the form $$y' = J(t)y + g(t,y)$$ where $$J(t)$$ is diagonalizable with a well-conditioned, smoothly varying eigensystem and $$g$$ is a Lipschitz-bounded nonlinearity.
Reviewer: E.Hairer (Genève)

### MSC:

 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34E13 Multiple scale methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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