Convergence and stability of the split-step backward Euler method for linear stochastic delay integro-differential equations

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Abstract

In this paper, we focus on the numerical approximation of solutions of linear stochastic delay integro-differential equations (SDIDEs). Split-step backward Euler (SSBE) method for solving linear stochastic delay integro-differential equations is derived. It is proved that the SSBE method is convergent with strong order γ = frac(1, 2) in the mean-square sense. The condition under which the SSBE method is mean-square stable (MS-stable) is obtained. At last some scalar test equations are simulated. The numerical experiments verify the results obtained from theory. © 2009 Elsevier Ltd. All rights reserved.

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Tan, J., & Wang, H. (2010). Convergence and stability of the split-step backward Euler method for linear stochastic delay integro-differential equations. Mathematical and Computer Modelling, 51(5–6), 504–515. https://doi.org/10.1016/j.mcm.2009.11.020

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