Improving split-step forward methods by ODE solver for stiff stochastic differential equations

Abstract

The present paper focuses on the improving split-step forward methods to solve of stiff stochastic differential equations of Itô type. These methods are based on the exponential modified Euler schemes. We show the convergency of our suggested explicit methods to solution of the corresponding stochastic differential equations in strong sense. For a test equation, mean-square stability of schemes are investigated. The numerical examples will be presented to support theoretical findings.

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Acknowledgements

This research was in part supported by the Research Council of Semnan University.

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Correspondence to K. Nouri.

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Nouri, K. Improving split-step forward methods by ODE solver for stiff stochastic differential equations. Math Sci (2021). https://doi.org/10.1007/s40096-021-00392-7

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Keywords

  • Itô stochastic differential equations
  • Euler-Maruyama method
  • Strong convergence
  • Mean-square stability

Mathematics Subject Classification

  • 34F05
  • 60H10
  • 41A25
  • 93E15