A New Efficient Explicit Scheme of Order $1.5$ for SDE with Super-linear Drift Coefficient

Abstract

We propose a new explicit numerical scheme for stochastic differential equation with super-linearly growing drift and linearly growing diffusion coefficients which are also twice continuously differentiable. The rate of strong convergence in $\mathcal{L}^p$-norm is shown to be equal to $1.5$. Moreover, the scheme is computationally more efficient that the corresponding scheme available in the literature.