The linear Steklov method for SDEs with non-globally Lipschitz coefficients: Strong convergence and simulation

We present an explicit numerical method for solving stochastic differential equations with non-globally Lipschitz coefficients. A linear version of the Steklov average under a split-step formulation supports our new solver. The linear Steklov method converges strongly with a standard one-half order. Also, we present numerical evidence that the explicit linear Steklov reproduces almost surely stability solutions with high-accuracy for diverse application models even for stochastic differential systems with super-linear diffusion coefficients.