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Numerics of stochastic parabolic differential equations with stable finite difference schemes | ||
| Iranian Journal of Science | ||
| مقاله 8، دوره 36، شماره 1، اردیبهشت 2012، صفحه 61-70 اصل مقاله (298.79 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2012.2057 | ||
| نویسندگان | ||
| A.R. Soheili* 1؛ M. Arezoomandan2 | ||
| 1Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 2Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran | ||
| چکیده | ||
| In the present article, we focus on the numerical approximation of stochastic partial differential equations of Itˆo type with space-time white noise process, in particular, parabolic equations. For each case of additive and multiplicative noise, the numerical solution of stochastic diffusion equations is approximated using two stochastic finite difference schemes and the stability and consistency conditions of the considered methods are analyzed. Numerical results are given to demonstrate the computational efficiency of the stochastic methods. | ||
| کلیدواژهها | ||
| Stochastic partial differential equations of Itˆo type؛ finite difference methods؛ multiplicative noise؛ additive noise؛ Saul’yev method؛ Liu method؛ convergence؛ consistency؛ Stability | ||
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