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In this paper, we consider scalar stochastic differential equations (SDEs)with a superlinearly growing and piecewise continuous drift coefficient.Existence and uniqueness of strong solutions of such SDEs are obtained.Furthermore, the classical $L_p$-error rate 1/2 for all $p\in [1, +\infty)$ isrecovered for the tamed Euler scheme. A numerical example is provided tosupport our conclusion.

Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient