Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations

Farkhonderooz, Omid; Ahmadian, Davood

doi:10.22034/cmde.2021.44264.1871

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	Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations
Computational Methods for Differential Equations
مقاله 5، دوره 10، شماره 3، مهر 2022، صفحه 617-638 اصل مقاله (462.44 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.44264.1871
نویسندگان
Omid Farkhonderooz؛ Davood Ahmadian^*
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
چکیده
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.
کلیدواژه‌ها
Stochastic differential equations؛ Stochastic Runge-Kutta schemes؛ Itˆo-Taylor expansion؛ Mean-square stability؛ Convergence

مراجع
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Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations