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Register a new userNumerical Simulation Stochastic of Differential Equations by Using Spline Function Approximations
محاكاة عددية للمعادلات التفاضلية العشوائية باستخدام تقريبات دالة شرائحية
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نقدم في هذا العمل محاكاة عددية للمعادلات التفاضلية العشوائية باستخدام تقريبات دالة شرائحية. تمت محاكاة عملية وينر العشوائية المستمرة مع الزمن كعملية منفصلة، ثم دراسة الاستقرار العشوائي المقارب للتقريبات الشرائحية مع خمس نقاط تجميع عندما تُطَبقْ مع عملية وينر لحل منظومات من المعادلات التفاضلية العشوائية. تبين الدراسة أن الطريقة تكون مستقرة و متقاربة عندما يتم تطبيقها لحل منظومة معادلات تفاضلية عشوائية خطية و غير خطية. و قد تم اختبار فعالية الطريقة المقترحة بحل مسألتي اختبار الأولى خطية و الثانية غير خطية، و تشير النتائج العددية إلى فعالية و كفاءة الطريقة الشرائحية المقترحة بالمقارنة مع طرائق أولر-مارياما، ميلستين، رانج-كوتا.
In this paper, spline approximations with five collocation points are used for the numerical simulation of stochastic of differential equations(SDE). First, we have modeled continuous-valued discrete wiener process, and then numerical asymptotic stochastic stability of spline method is studied when applied to SDEs. The study shows that the method when applied to linear and nonlinear SDEs are stable and convergent. Moreover, the scheme is tested on two linear and nonlinear problems to illustrate the applicability and efficiency of the purposed method. Comparisons of our results with Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the our scheme is better than others.
References used
(HIGHAM D. J., An Algorithmic Introduction to Numerical Simulation of Stochastic Differential, Society for Industrial and Applied Mathematics, Vol. 43,No . 3,pp . 525–546 (2001
TOCINO A., R. Ardanuy, Runge–Kutta methods for numerical solution of stochastic differential equations, Journal of Computational and Applied Mathematics 138 (2002) 219–241
WANG P., Three-stage stochastic Runge–Kutta methods for stochastic differential equations, Journal of Computational and Applied Mathematics 222 (2008) 324–332
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