Mean Square Heun’s Method Convergent for Solving Random Differential Initial Value Problems of First Order
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Author(s)
This paper deals with the construction of Heun’s
method of random initial value problems. Sufficient conditions for their
mean square convergence are established. Main statistical properties of
the approximations processes are computed in several illustrative
examples.
KEYWORDS
Cite this paper
Sohaly, M. (2014) Mean Square Heun’s Method
Convergent for Solving Random Differential Initial Value Problems of
First Order. American Journal of Computational Mathematics, 4, 474-481. doi: 10.4236/ajcm.2014.45040.
| [1] |
Burrage, K. and Burrage, P.M.
(1996) High Strong Order Explicit Runge-Kutta Methods for Stochastic
Ordinary Differential Equations. Applied Numerical Mathematics, 22,
81-101. http://dx.doi.org/10.1016/S0168-9274(96)00027-X |
| [2] |
Burrage, K. and Burrage, P.M.
(1998) General Order Conditions for Stochastic Runge-Kutta Methods for
Both Commuting and Non-Commuting Stochastic Ordinary Equations. Applied
Numerical Mathematics, 28, 161-177.
http://dx.doi.org/10.1016/S0168-9274(98)00042-7 |
| [3] |
Cortes, J.C., Jodar, L. and
Villafuerte, L. (2007) Numerical Solution of Random Differential
Equations, a Mean Square Approach. Mathematical and Computer Modeling,
45, 757-765. http://dx.doi.org/10.1016/j.mcm.2006.07.017 |
| [4] | Cortes, J.C., Jodar, L. and Villafuerte, L. (2006) A Random Euler Method for Solving Differential Equations with Uncertainties. Progress in Industrial Mathematics at ECMI. |
| [5] |
Lamba, H., Mattingly, J.C. and
Stuart, A. (2007) An Adaptive Euler-Maruyama Scheme for SDEs,
Convergence and Stability. IMA Journal of Numerical Analysis, 27,
479-506. http://dx.doi.org/10.1093/imanum/drl032 |
| [6] |
Platen, E. (1999) An
Introduction to Numerical Methods for Stochastic Differential Equations.
Acta Numerica, 8, 197-246. http://dx.doi.org/10.1017/S0962492900002920 |
| [7] |
Higham, D.J. (2001) An
Algorithmic Introduction to Numerical Simulation of SDE. SIAM Review,
43, 525-546.
http://dx.doi.org/10.1137/S0036144500378302 |
| [8] |
Talay, D. and Tubaro, L. (1990)
Expansion of the Global Error for Numerical Schemes Solving Stochastic
Differential Equation. Stochastic Analysis and Applications, 8, 483-509.
http://dx.doi.org/10.1080/07362999008809220 |
| [9] | Burrage, P.M. (1999) Numerical Methods for SDE. Ph.D. Thesis, University of Queensland, Brisbane. |
| [10] | Kloeden, P.E., Platen, E. and Schurz, H. (1997) Numerical Solution of SDE through Computer Experiments. 2nd Edition, Springer, Berlin. |
| [11] |
El-Tawil, M.A. (2005) The
Approximate Solutions of Some Stochastic Differential Equations Using
Transformation. Applied Mathematics and Computation, 164, 167-178. http://dx.doi.org/10.1016/j.amc.2004.04.062 |
| [12] |
El-Tawil, M.A. and Sohaly, M.A.
(2011) Mean Square Numerical Methods for Initial Value Random
Differential Equations. Open Journal of Discrete Mathematics, 1, 66-84. http://dx.doi.org/10.4236/ojdm.2011.12009 |
| [13] | Kloeden, P.E. and Platen, E. (1999) Numerical Solution of Stochastic Differential Equations. Springer, Berlin. eww141230lx |
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