@article { author = {Farkhonderooz, Omid and Ahmadian, Davood}, title = {Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations}, journal = {Computational Methods for Differential Equations}, volume = {10}, number = {3}, pages = {617-638}, year = {2022}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {10.22034/cmde.2021.44264.1871}, 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 = {Stochastic differential equations,Stochastic Runge-Kutta schemes,Itˆo-Taylor expansion,Mean-square stability,Convergence}, url = {https://cmde.tabrizu.ac.ir/article_12795.html}, eprint = {https://cmde.tabrizu.ac.ir/article_12795_c5199f6a32b034e1c1877a73f3c76cc6.pdf} }