Norhayati, Rosli and Noor Julailah, Abd Mutalib and Noor Amalina Nisa, Ariffin and Mazma Syahidatul Ayuni, Mazlan (2019) The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations. In: AIP Conference Proceedings; 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018 , 10 - 12 December 2018 , Penang, Malaysia. , 2184 (060051). ISSN 0094-243X ISBN 9780735419315
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Abstract
This paper is devoted to investigate the performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations (SDDEs) in population dynamics. The corresponding deterministic models of population dynamics follow the generalised of Verhults laws. Stochastic Taylor methods for SDDEs are developed by truncating the stochastic Taylor series expansion with time delay at certain order. As the order increasing, the method is proving theoretically will provide better solutions for SDDEs. However, the difficulty arises in implementing the stochastic Taylor methods as one needs to find the partial derivative of drift and diffusion functions. It is then natural to look for derivative-free method. This paper demonstrates the performance of the existing stochastic Taylor methods of Euler Maruyama and Milstein scheme and the derivative-free method of 1.0 order of convergence in approximating the solutions of SDDEs models under Verhutls laws. Numerical experiments are conducted to demonstrate the performance of the corresponding methods in approximating the solutions of SDDEs.
| Item Type: | Conference or Workshop Item (Poster) |
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| Additional Information: | Indexed by Scopus |
| Uncontrolled Keywords: | Stochastic Taylor methods; Derivative-free method; Stochastic delay differential equations (SDDEs); Population dynamics |
| Subjects: | T Technology > T Technology (General) T Technology > TA Engineering (General). Civil engineering (General) |
| Faculty/Division: | Center for Mathematical Science |
| Depositing User: | Mrs Norsaini Abdul Samat |
| Date Deposited: | 18 Jun 2020 02:31 |
| Last Modified: | 18 Jun 2020 02:31 |
| URI: | http://umpir.ump.edu.my/id/eprint/27730 |
| Download Statistic: | View Download Statistics |
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