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In this paper, we are interested in the time discrete approximation ofEf(X(T)) when X is the solution of a stochastic differential equation with adiffusion coefficient function of the form |x|^a. We propose a symmetrizedversion of the Euler scheme, applied to X. The symmetrized version is very easyto simulate on a computer. For smooth functions f, we prove the Feynman Kacrepresentation u(t,x) = E_{t,x} f(X(T)), for u(t,x) solving the associatedKolmogorov PDE and we obtain the upper-bounds on the spatial derivatives of uup to the order four. Then we show that the weak error of our symmetrizedscheme is of order one, as for the classical Euler scheme.

Weak convergence analysis of the symmetrized Euler scheme for one dimensional SDEs with diffusion coefficient |x|^a, a in [1/2,1)