Küçük Gürültü Terimi İçeren Itô Stokastik Diferansiyel Denklemler için Stokastik Runge-Kutta-Fehlberg Yöntemi

Year 2020, Volume: 13 Issue: 2, 898 - 916, 31.08.2020

Hande Akdemir Dudu Aydın Oğur

https://doi.org/10.18185/erzifbed.617161

Abstract

Bu
çalışmada, difüzyon teriminde küçük bir çarpan olan Itô stokastik diferansiyel
denklemler (SDD) için stokastik Runge-Kutta-Fehlberg yöntemi (SRKFY)
önerilmiştir. Bu yöntem, deterministik diferansiyel denklemler için iyi bilinen
ve türevleri kullanmayan altı aşamalı RKFY’nin karışık stokastik
(klasik-stokastik) integralleri kullanan bir uyarlamasıdır. Önerilen yöntemin
ara adımlarında Euler-Maruyama tahminleyicisi kullanılmıştır. Bazı test
problemleri için, yöntemin kuadratik orta anlamda yakınsaklığını incelemek ve
bilinen bazı yöntemlerle karşılaştırmak amacıyla simülasyon çalışmaları
yapılmıştır.

Keywords

Runge-Kutta-Fehlberg yöntemi, Itô stokastik diferansiyel denklemler, nümerik çözümler, küçük gürültü

Supporting Institution

Giresun Üniversitesi Bilimsel Araştırma Projeleri Birimi

Project Number

FEN-BAP-A-230218-49

Thanks

Bu çalışma, Giresun Üniversitesi Bilimsel Araştırma Projeleri Birimi tarafından desteklenmiştir (Proje No: FEN-BAP-A-230218-49).

A Stochastic Runge-Kutta-Fehlberg Method for Itô Stochastic Differential Equations with Small Noise

Abstract

In this study, a stochastic Runge-Kutta-Fehlberg (SRKF) method is proposed for the Itô stochastic differential equations (SDE) with a small factor in the diffusion coefficient. This method, which uses mixed stochastic (classical-stochastic) integrals, is an extension of derivative-free six-stage RKF method which is well known for deterministic DE. In intermediate steps of the proposed method, the Euler-Maruyama predictor is used. For some test problems, simulation studies are conducted to examine strong convergence of the method and compare it with some known methods

Keywords

Runge-Kutta-Fehlberg method,, Itô stochastic differential equations, numerical solutions

Project Number

FEN-BAP-A-230218-49

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