DOI: https://doi.org/10.14710/jfma.v3i1.7416

NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD

*Ratna Herdiana  -  Department of Mathematics, Diponegoro University, Indonesia

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Abstract
Stiff stochastic differential equations arise in many applications including in the area of biology. In this paper, we present numerical solution of stochastic differential equations representing the Malthus population model and SIS epidemic model, using the improved implicit Milstein method of order one proposed in [6]. The open source programming language SCILAB is used to perform the numerical simulations. Results show that the method is more accurate and stable compared to the implicit Euler method.
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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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  3. E. J. Allen, "Stochastic Differential Equations and persistence Time for Two Interacting Populations", Dyn.Cont., Discrete and Impulsive System, 5, pp. 271 - 281, 1999
  4. G.N. Milstein, "Numerical Integration of Stochastic Differential Equatuions", Springer Science and Business Media, 1994
  5. G.N. Milstein, E. Platen, H. Schurz: Balanced implicit methods for stiff stochastic systems. SIAM J. Numer. Anal. 35(3), 1010-1019 (1998)
  6. G. Maruyama, "Continuos Markov Process and Stochastic Equations", Rend.Circolo, Math. Parlermo 4(1),1955, 48 - 90
  7. Jinran Yao, Siqing Gan, "Stability of Drift-Implicit and Double -Implicit Milstein Schemes for Nonlinear Stochastic Diffrential Equations", J. Applied Mathematics and Computation, Vol.339, 2018, pp. 294-301
  8. K. Burrage and T. Tian, "A Note on the Stability Properties of the Euler Methods for Solving Stochastic Differential Equations", New Zealand Journal of Mathematics, Vol. 29, pp.115 - 127, 2000
  9. K. Burrage, Tian, T, "The composite Euler method for stiff stochastic differential equations". J. Comput. Appl. Math. 131(1-2), 407-426 (2001)
  10. ] M.A. Omar, A. Aboul Hassan, S.I. Rabia, "The CompositeMilstein methods for numerical solution of Ito Stochastic Differential Equations", Journal of Computaional and Applied Mathematics, Vol.235, 2011, pp.2277-2299
  11. P.E. Kloeden and E. Platen, "The numerical solution of stochastic differential equations", Springer, Berlin, 1999
  12. X. Mao, "Stochastic Differential Equations and Applications", Howard Publishing Limited, Chichester, 2007
  13. Z. Yin and S. Gan, "An Improved Milstein Method for Stiff Stochastic Differential Equations", Springer Open Journal, Advances in Difference Equations: 369, 2015

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