Open AccessPerformance of 5-stage, 4-stage and specific stochastic Runge-Kutta methods in approximating the solution of stochastic biological model
Author(s) -
Noor Amaliisa Ariffin,
Norhayati Rosli,
Abdul Rahman Mohd Kasim,
Mazma Syahidatul Ayuni Mazlan
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1988/1/012008
Subject(s) - stochastic differential equation , runge–kutta methods , ordinary differential equation , stochastic modelling , mathematics , runge–kutta method , stochastic partial differential equation , continuous time stochastic process , stochastic process , numerical analysis , computer science , differential equation , mathematical optimization , mathematical analysis , differential algebraic equation , statistics
In recent years, the transition on modelling physical systems via stochastic differential equations (SDEs) has attracted great interest among researchers. This is due to the limitations of ordinary differential equations in presenting the real phenomenon. To the fact that the stochastic models incorporate the random effects that may influence the behaviour of physical systems, SDEs seems to be the best model that can be used i n assessing those systems. The growing interest among researchers in modelling the systems via SDEs comes with the rise in the need of numerical methods to approximate the solutions for SDEs. This is because by taking into account the random fluctuations in SDEs resulting to the complexity of finding the exact solution of SDEs. Therefore, it contribute to the increasing number of research to decide on the best numerical approach to solve the systems of SDEs. This paper is devoted to investigate the performance of 5-stage stochastic Runge-Kutta ( SRK5) with order 2.0, 4-stage stochastic Runge-Kutta ( SRK4), specific stochastic Runge-Kutta with order 1.5 ( SRKS1.5) and commutative specific stochastic Runge-Kutta with order 1.5 (SRKST2) in approximating the solution of stochastic model in biological system. A comparative study of SRK5, SRK4, SRKS1.5 and SRKST2 methods will be presented in this paper. The linear SDE model and the stochastic model of C. Acetobutylicum cell growth will be used to examine the performance of those methods and the numerical experiment will be conducted. The numerical solutions obtained will be discussed.