NUMERICAL SOLUTIONS TO CERTAIN STOCHASTIC DIFFERENTIAL EQUATIONS BY USING MILSTEIN METHOD
Keywords:
Numerical Solutions, Certain Stochastic Differential Equations, Milstein method, strongly convergence
Abstract
In this paper, we studied the numerical method to solve the stochastic differential equations. The Milstein method was used because of the difficulty of finding analytical solutions for many of Stochastic differential equations. Numerical simulations for different selected examples are implemented. In addition, the strong convergence error, are supported by numerical tests problems.
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References
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Bernard P. and Fleury G., "Convergence of schemes for stochastic differential equations; Monte Carlo methods", Applied, Vol.7(1), 35-53,( 2001).
Burrage K, Burrage PM, Tian T., "Numerical methods for strong solutions of stochastic differential equations": an overview. Proc .Roy. Soc .London ,(2004).
Burrage K. and Burrage P. M., "High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations", Applied Numerical Mathematics, Vol.22, 81-101, (1996).
Evans, L. C. , "An Introduction to stochastic differential equations", Version 1.2, Lecture Notes, Short Course at SIAM Meeting, July, (2005).
Fridman, A.F., "Stochastic differential equations and applications",V1, Academic Press, Inc., (1975).
Gard, T. G. , "Introduction to Stochastic Differential Equations", Marcel Dekker, New York, (1988).
Kloeden& Platen, "Numerical Solution of Stochastic Differential Equations",V.23, Applications of Mathematics, New York, Springer-Verlag, Berlin, (1992).
Romisch W, Winkler R," Step size control for mean-square numerical methods for stochastic differential equations with small noise". SIAM J Sci Comp 28 , (2006).
Raphael Kruse, Yue Wu, "randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients" ,submitted on 29 Jun 2017 (v1 )31 ,(2017).
Tocino A, Ardanuy R ," Runge-Kutta methods for numerical solution of stochastic differential equations".
J Comp Appl Math .,(2004).
Published
2018-11-15
How to Cite
HUSSAIN, A. S. (2018). NUMERICAL SOLUTIONS TO CERTAIN STOCHASTIC DIFFERENTIAL EQUATIONS BY USING MILSTEIN METHOD. Journal of Duhok University, 21(1), 121-128. https://doi.org/10.26682/sjuod.2018.21.1.12
Section
Pure and Engineering Sciences
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