| Stochastic Runge-Kutta Rosenbrock type scheme with strong global order one for stochastic differential equations |
| کد مقاله : 1044-FEMATH6 |
| نویسندگان |
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کاظم نوری *1، حسن رنجبر2، لیلا ترک زاده1 1هیات علمی گروه ریاضی دانشکده ریاضی، آمار و علوم کامپیوتر دانشگاه سمنان 2گروه ریاضی دانشگاه سمنان |
| چکیده مقاله |
| The analytical investigations and numerical solutions of stochastic differential equations have always been of interest to researchers. During the several decades, many efficient methods have been developed for solving different types of stochastic differential equations with different properties. We need numerical methods because a lot of stochastic differential equations are not analytically solvable. There are two dominating versions of stochastic calculus, the Ito stochastic calculus and the Stratonovich stochastic calculus. In this work, we concern the new class of stochastic Runge-Kutta method for solution of Stratonovich stochastic differential equations with scalar noise. Using Rosenbrock ordinary differential equation solver, we define stochastic Runge-Kutta Rosenbrock type scheme. In recent years, implicit stochastic Runge–Kutta methods have been developed both for strong and weak approximations. For these methods, the stage values are only given implicitly. Stratonovich Taylor expansion is applied to derive strong global convergence order 1.0. Also, mean-square stability is studied and some examples are presented to support the theoretical results. |
| کلیدواژه ها |
| Stochastic Runge-Kutta Rosenbrock scheme, Stratonovich stochastic differential equations, Stratonovich Taylor expansion, Strong global order, Mean-square stability. |
| وضعیت: پذیرفته شده برای ارائه شفاهی |