In this paper we consider a general class of stochastic differential equations driven by stable processes with continuous coefficients functions with at most linear growth. An Euler-Maruyama approximate solution is proved as well as the rate of convergence. Our proposed method is new in this context and is based on a level truncation method by separating the large and small jumps of the stable process along the Lévy-Itô decomposition. Along the paper we give some numerical simulations of stochastic models that agree with our results, namely some stable driven Ornstein-Uhlenbeck, Cox-Ingersoll-Ross and Lotka-Volterra type processes.
AMS Subject Classification: 60G17, 60G52, 60H10, 60H20, 65C30, 65C20, 60E07.