Euler scheme for approximation of solution of nonlinear ODEs under inexact information
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We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-side Lipschitz condition and local Hölder continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Lastly, we present the results of some numerical experiments.
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