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This paper is concerned with the numerical analysis of the explicit Eulerscheme for ordinary differential equations with non-Lipschitz vector fields. Weprove the convergence of the Euler scheme to regular lagrangian flow(Diperna-Lions flows) which is the right concept of the solution in thiscontext. Moreover, we show that order of convergence is $\frac{1}{2}$.

Discretization by euler's method for regular lagrangian flow