On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth

We consider the problem of designing robust numerical integration scheme solution a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients behaving as $x^{\alpha }$, $\alpha >1$. propose an (semi-explicit) exponential-Euler for which we obtain theoretical convergence rate weak error. To this aim, analyze $C^{1,4}$ regularity associated backward Kolmogorov PDE using its Feynman–Kac representation flow derivative involved processes. Under some suitable hypotheses on parameters model, prove order one proposed exponential Euler scheme, illustrate it experiments.