Buckwar, Evelyn Introduction to the numerical analysis of stochastic delay differential equations. (English) Zbl 0971.65004 J. Comput. Appl. Math. 125, No. 1-2, 297-307 (2000). This paper concerns the numerical approximation of the strong solution of the Itô stochastic delay differential equation (SDDE) \[ dX(t)=f(X(t),X(t-\tau))dt+g(X(t),X(t-\tau))dW(t),\quad t\in[0,\tau], \] where \(X(t) =\psi(t)\), \(t\in [-\tau,0]\) and \(W(t)\) is a Wiener process. A theorem is proved establishing conditions for convergence, in the mean-square sense, of approximate solutions obtained from explicit single-step methods. Then a SDDE version of the Euler-Maruyama method is presented and found to have order of convergence 1. The paper concludes with several figures illustrating numerical results obtained when this method is applied to an example. Reviewer: Melvin D.Lax (Long Beach) Cited in 94 Documents MSC: 65C30 Numerical solutions to stochastic differential and integral equations 34K50 Stochastic functional-differential equations 34F05 Ordinary differential equations and systems with randomness 65H10 Numerical computation of solutions to systems of equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations Keywords:strong solution; Ito stochastic delay differential equation; convergence; explicit single-step methods; Euler-Maruyama method; numerical results PDFBibTeX XMLCite \textit{E. Buckwar}, J. Comput. Appl. Math. 125, No. 1--2, 297--307 (2000; Zbl 0971.65004) Full Text: DOI References: [1] Arnold, L., Stochastic Differential Equations: Theory and Applications (1974), Wiley-Interscience: Wiley-Interscience New York [2] C.T.H. Baker, E. 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