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A class of split-step balanced methods for stiff stochastic differential equations

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Abstract

In this paper we design a class of general split-step balanced methods for solving Itô stochastic differential systems with m-dimensional multiplicative noise, in which the drift or deterministic increment function can be taken from any chosen one-step ODE solver. We then give an analysis of their order of strong convergence in a general setting, but for the mean-square stability analysis, we confine our investigation to a special case in which the drift increment function of the methods is replaced by the one from the well known Rosenbrock method. The resulting class of stochastic differential equation (SDE) solvers will have more appropriate and useful mean-square stability properties for SDEs with stiffness in their drift and diffusion parts, compared to some other already reported split-step balanced methods. Finally, numerical results show the effectiveness of these methods.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran

    Amir Haghighi & S. Mohammad Hosseini

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  1. Amir Haghighi
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  2. S. Mohammad Hosseini
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Correspondence to Amir Haghighi.

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Haghighi, A., Hosseini, S.M. A class of split-step balanced methods for stiff stochastic differential equations. Numer Algor 61, 141–162 (2012). https://doi.org/10.1007/s11075-012-9534-5

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  • DOI: https://doi.org/10.1007/s11075-012-9534-5

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