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

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

References

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Computational Methods for Differential Equations
Volume 10, Issue 3
July 2022
Pages 617-638

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History

  • Receive Date: 28 January 2021
  • Accept Date: 01 May 2021

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