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In this paper, we will study and introduce the higher-order weak variable order methods for approximation the solution of functionals diffusion of Ito kind. Under appropriate regularity conditions, it is shown that variable order method allows a considerable increase in the weak order of convergence of a discrete time one step approximation method. Numerical method experiments indicate the efficiency of variable order based on higher-order weak scheme for stochastic ordinary differential equations with additive noise.

Variable Order Linear Multi-Step Methods for Solving Stochastic Ordinary Differential Equations