Lipschitz condition the compensated tamed Euler scheme converges strongly with standard order $0.5$. Inspired by [@Xia2], we propose the semi-tamed Euler for SDEs with jumps under non-global Lipschitz condition and prove its strong convergence of order $0.5$. This latter result is helpful to prove the strong convergence of the tamed Euler scheme. We analyse the stability behaviours of both tamed and semi-tamed Euler scheme We present also some numerical experiments to illustrate our theoretical results.\
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**Key words** : Stochastic differential equation, strong convergence, mean-square stability, Euler scheme, global Lipschitz condition, polynomial growth condition, one-sided Lipschitz condition.

Declaration {#declaration .unnumbered}
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I, the undersigned, hereby declare that the work contained in this essay is my original work, and that any work done by others or by myself previously has been acknowledged and referenced accordingly.

![image](signjd.jpg)

Jean Daniel Mukam, 25 May 2015

INTRODUCTION {#introduction .unnumbered}
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In many branches of sciences like finance, economics, biology, engineering, ecology one often encountered some problems influenced by uncertainties. For example, in finance, the unpredictable nature of events such as markets crashes and booms may have significant and sudden impact on the stock price fluctuations. Therefore, in order to have more realistic prediction of these 