Document Type : Research Paper

**Authors**

Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

**Abstract**

In this paper, we are interested in the construction of an explicit third-order stochastic Runge–Kutta (SRK3) schemes for the weak approximation of stochastic differential equations (SDEs) with the general diffusion coefficient b(t, x). To this aim, we use the Itˆo-Taylor method and compare them with the stochastic expansion of the approximation. In this way, the authors encountered a large number of equations and could find to derive four families for SRK3 schemes. Also, we investigate the mean-square stability (MS-stability) properties of SRK3 schemes for a linear SDE. Finally, the proposed families are implemented on some examples to illustrate convergence results.

**Keywords**

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July 2022

Pages 617-638

**Receive Date:**28 January 2021**Accept Date:**01 May 2021**First Publish Date:**01 May 2021