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Euler’s method revisited. (English. Russian original) Zbl 0872.65075
Proc. Steklov Inst. Math. 211, 429-449 (1995); translation from Tr. Mat. Inst. Steklova 211, 473-494 (1995).
We concentrate on explicit difference methods for differential inclusions not satisfying the usual Lipschitz condition, e.g. differential inclusions modelling certain types of differential equations which are discontinuous with respect to the state variables. We investigate a class of right-hand sides, satisfying a so-called strengthened one-sided Lipschitz condition. This condition, weaker than the classical Lipschitz condition for single-valued right-hand sides, but stronger than the usual one-sided Lipschitz condition, is the essential tool for our order of convergence analysis.
For the entire collection see [Zbl 0863.00015].

MSC:
65L12 Finite difference and finite volume methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34A60 Ordinary differential inclusions
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