Stability analysis of explicit and semi-implicit derivative-free methods for stochastic differential equations

• Main Authors: Norhayati, Rosli, Noor Amalina Nisa, Ariffin
• Format: Article
• Language: English
• Published: UTM Press 2016
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/20731/1/Stability%20analysis%20of%20explicit%20and%20semi-implicit%20derivative-free.pdf; http://umpir.ump.edu.my/id/eprint/20731/; http://www.utm.my/ispc2016/ispc2016-proceedings-book/
• Institution: Universiti Malaysia Pahang

This paper is devoted to investigate the mean-square stability of explicit and semi-implicit derivative-free methods to a class of stochastic differential equations (SDEs). The mean-square stability functions and regions of explicit and semi-implicit numerical approximation schemes are obtained for a linear stochastic differential equation with multiplicative noise. It is proved that the semi-implicit derivative-free method is mean-square stable compare than the explicit counterpart schemes. A numerical experiment is provided to illustrate the theory.