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Improved Euler–Maruyama Method for Numerical Solution of the Itô Stochastic Differential Systems by Composite Previous-Current-Step Idea

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Abstract

In this paper, by composite previous-current-step idea, we propose two numerical schemes for solving the Itô stochastic differential systems. Our approaches, which are based on the Euler–Maruyama method, solve stochastic differential systems with strong sense. The mean-square convergence theory of these methods are analyzed under the Lipschitz and linear growth conditions. The accuracy and efficiency of the proposed numerical methods are examined by linear and nonlinear stochastic differential equations.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box 35195-363, Semnan, Iran

    Kazem Nouri, Hassan Ranjbar & Leila Torkzadeh

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Kazem Nouri

Authors
  1. Kazem Nouri
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  2. Hassan Ranjbar
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  3. Leila Torkzadeh
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Corresponding author

Correspondence to Kazem Nouri.

Additional information

This research was in part supported by a Grant from IPM (No. 94650074), and in part by the Research Council of Semnan University.

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Nouri, K., Ranjbar, H. & Torkzadeh, L. Improved Euler–Maruyama Method for Numerical Solution of the Itô Stochastic Differential Systems by Composite Previous-Current-Step Idea. Mediterr. J. Math. 15, 140 (2018). https://doi.org/10.1007/s00009-018-1187-8

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  • DOI: https://doi.org/10.1007/s00009-018-1187-8

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