In this research we explore two numerical approaches for simulating the stochastic differential equations (SDEs) with Lévy noise. This study focus on a stochastic logistic equation (SLE) by two independent Lévy processes. The research assesses the Tamed Euler and ε–Euler–Maruyama methods, both method ware designe for SDEs with nonlinear coefficient. To measure their performance, two generally used error metrics—Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are employed. Result shows that, the Tamed Euler scheme tends to produce more accurate approximations. Owing to, in cases involving strong noise and larger time step size, the ε–Euler–Maruyama method has better performace than Tamed approach. The investigation further examines how different parameters affect the precision and stability of each method. The results prove that both schemes are effective and suitable for numerically solving SDEs with Lévy noise.