Discretization by euler's method for regular lagrangian flow

2019/09/24 by Londoño, Juan D., Olivera, Christian
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1909.11122

Abstract

This paper is concerned with the numerical analysis of the explicit Euler scheme for ordinary differential equations with non-Lipschitz vector fields. We prove the convergence of the Euler scheme to regular lagrangian flow (Diperna-Lions flows) which is the right concept of the solution in this context. Moreover, we show that order of convergence is (1)/(2).

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