Mean Square Numerical Methods for Initial Value Random Differential Equations

In this paper, the random Euler and random Runge-Kutta of the second order methods are used in solving random differential initial value problems of first order. The conditions of the mean square convergence of the numerical solutions are studied. The statistical properties of the numerical solutions are computed through numerical case studies.

[1]  N. Bershad,et al.  Random differential equations in science and engineering , 1975, Proceedings of the IEEE.

[2]  D. Talay,et al.  Expansion of the global error for numerical schemes solving stochastic differential equations , 1990 .

[3]  Jonathan C. Mattingly,et al.  An adaptive Euler–Maruyama scheme for SDEs: convergence and stability , 2006, math/0601029.

[4]  Neil J. Bershad,et al.  Review of 'Random Differential Equations in Science and Engineering' (Soong, T. T.; 1973) , 1975, IEEE Transactions on Information Theory.

[5]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[6]  P. Kloeden,et al.  Numerical Solution of Sde Through Computer Experiments , 1993 .

[7]  Juan Carlos Cortés,et al.  Mean square numerical solution of random differential equations: Facts and possibilities , 2007, Comput. Math. Appl..

[8]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[9]  K. Burrage,et al.  High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations , 1996 .

[10]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of , 2001 .

[11]  L. Villafuerte,et al.  A Random Euler Method for Solving Differential Equations with Uncertainties , 2008 .

[12]  Magdy A. El-Tawil,et al.  The approximate solutions of some stochastic differential equations using transformations , 2005, Appl. Math. Comput..

[13]  E. Platen.  An introduction to numerical methods for stochastic differential equations , 1999, Acta Numerica.

[14]  Kevin Burrage,et al.  General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems , 1998 .