Numerical Solutions of Stochastic Differential Equations by using Heun's method


  • Adel S. Hussain Amedey Institute, Duhok Polytechnic University, Kurdistan Region of Iraq



Numerical Solutions, Stochastic Differential Equations Heun's numerical method


In this work, we   study  the numerical method for solving Stochastic differential equations. Because of the difficulty of finding analytical solutions for many of the Stochastic differential equations the Heun's method  was used. Numerical simulations for different selected  examples are implemented. And the difference between the numerical solution and the exact solution was also found.


Download data is not yet available.


1. Abdu Khaled M, (2004)., "Mean Square Stability of Second-Order Weak Numerical Methods for Stochastic Differential Equations", Applied Numerical Mathematics, Vo.48, 127-134.
2. Arnold J. ,(1974), "Stochastic Differential Equations; Theory and Applications", John Wiley and Sons, New York.
3. Bernard P. and Fleury G. ,(2001), "Convergence of Schemes for Stochastic Differential Equations; Monte Carlo Methods", Applied, Vol.7(1), 35-53.
4. Burrage K. and Burrage P. M. ,(1996), "High Strong Order Explicit Runge-Kutta Methods for Stochastic Ordinary Differential Equations", Applied Numerical Mathematics, Vol.22, 81-101.
5. Evans,(2005): Lawrence C. Evance, "An Introduction to Stochastic Differential Equations", Version 1.2, Lecture Notes, Short Course at SIAM Meeting, July, 2005.
6. Fridman,(1975) : AvnerFridman, "Stochastic Differential Equations and Applications", Volume 1, Academic Press, Inc., 1975.
7. Kloeden& Platen, (1992) : P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations", V.23, Applications of Mathematics, New York, Springer-Verlag, Berlin, 1992.
8. Gard, T. G. Gard, (1988). "Introduction to Stochastic Differential Equations", Marcel Dekker, New York, (1988).
9. Glasserman P,Monte Carlo methods in _numerical engineering. Springer, New York(2004).
10. Higham DJ,An algorithmic introduction to numerical simulation of stochastic differential equation,s(2001).
11. Higham DJ, Kloeden P,Numerical methods for nonlinear stochastic differential equations with jumps. Num Math.,(2005).
12. Jentzen A, Kloeden P,Neuenkirch A,Pathwise approximation of stochastic differential equations on domains :
13. higher order convergence rates without global Lipschitz coe_cients. Num Math.,(2008).
14. Kloeden P, Platen E, Schurz H,Numerical solution of SDE through computer experiments. Springer, Berlin,(1994).
15. Lamba H, Mattingly JC, Stuart A,An adaptive Euler-Maruyama scheme for SDEs : convergence and stability.(2008).
16. Milstein G.,Numerical integration of stochastic differential equations Kluwer, Dordrecht, (1995).



How to Cite

Hussain, A. S. (2018). Numerical Solutions of Stochastic Differential Equations by using Heun’s method. Academic Journal of Nawroz University, 7(3), 208–215.