Derivation of stochastic Taylor methods for stochastic differential equations by Noor Amalina Nisa, Ariffin, Norhayati, Rosli

“…This paper demonstrates a derivation of stochastic Taylor methods for stochastic differential equations (SDEs). The stochastic Taylor series is extended and truncated at certain terms to achieve the order of convergence of stochatsic Taylor methods for SDEs. …”
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Fifth-stage stochastic runge-kutta method for stochastic differential equations by Noor Amalina Nisa, Ariffin

“…Hence, models for these systems are required via stochastic differential equations (SDEs). However, it is often difficult to find analytical solutions of SDEs. …”
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Stability Analysis of Explicit and Implicit Stochastic Runge-Kutta Methods for Stochastic Differential Equations by Adam, Samsudin, Norhayati, Rosli, Amalina Nisa, Ariffin

“…The stability analysis of the schemes in mean-square norm is investigated. Linear stochastic differential equations are used as test equations to demonstrate the efficiency of the proposed schemes.…”
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Stability analysis of explicit and semi-implicit derivative-free methods for stochastic differential equations by Norhayati, Rosli, Noor Amalina Nisa, Ariffin

“…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. …”
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Comparative study of stochastic Taylor methods and derivative-free methods for stochastic differential equations by Muhammad Fahmi, Ahmad Zuber, Norhayati, Rosli

“…However, modelling these systems using deterministic model such as ODEs is inadequate as the system is subjected to the uncontrolled factors of environmental noise. Stochastic differential equations (SDEs) which are originating from the irregular Brownian motion can be applied to model such systems that subjected to the uncontrolled factors of noisy behaviour. …”
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Modelling the cancer growth process by stochastic differential equations with the effect of chondroitin sulfate (cs) as anticancer therapeutics by Mazma Syahidatul Ayuni, Mazlan, Norhayati, Rosli, Nina Suhaity, Azmi, Solachuddin Jauhari, Arief Ichwan

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Adaptive step size stochastic runge-kutta method of order 1.5(1.0) for stochastic differential equations (SDEs) by Noor Julailah, Abd Mutalib, Norhayati, Rosli, Noor Amalina Nisa, Ariffin

“…The stiff stochastic differential equations (SDEs) involve the solution with sharp turning points that permit us to use a very small step size to comprehend its behavior. …”
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Parameter estimation of the stochastic model for oral cancer in response to thymoquinone (TQ) as anticancer therapeutics by Tabassum, Shabana, Rosli, Norhayati, Jauhari Arief, Solachuddin

“…This article models the decelerating of the oral cancer growth by using a linear stochastic differential equation (SDEs). The Markov Chain Monte Carlo (MCMC) method used to estimate model parameters for 100, 500,1000 and 2000 simulations. …”
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Performance of stochastic Runge-Kutta Methods in approximating the solution of stochastic model in biological system by Noor Amalina Nisa, Ariffin, Norhayati, Rosli, Mazma Syahidatul Ayuni, Mazlan, Adam, Samsudin

“…Recently, modelling the biological systems by using stochastic differential equations (SDEs) are becoming an interest among researchers. …”
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Modelling the cervical cancer growth process by stochastic delay differential equations by Mazma Syahidatul Ayuni, Mazlan, Norhayati, Rosli, Nina Suhaity, Azmi, Arifah, Bahar

“…The growth process under Gompertz’s law is considered, thus lead to stochastic differential equations of Gompertzian with time delay. …”
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Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262 by Tawfiqullah, Ayoubi

“…Ordinary differential equations (ODEs) and stochastic differential equations (SDEs) are widely used to model biological systems in the last decades. …”
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Stochastic Runge-Kutta method for stochastic delay differential equations by Norhayati, Rosli

“…However,the complexity arises due to the presence of both randomness and time delay.The analytical solution of SDDEs is hard to be found.In such a case, a numerical method provides a way to solve the problem.Nevertheless, due to the lacking of numerical methods available for solving.SDDEs,a wide range of researchers among the mathematicians and scientists have not incorporated the important features of the real phenomena,which include randomness and time delay in modeling the system.Hence,this research aims to generalize the convergence proof of numerical methods for SDDEs when the drift and diffusion functions are Taylor expansion and to develop a stochastic Runge—Kutta for solving SDDEs Motivated by the relative paucity of numerical methods accessible in simulating the strong solution of SDDEs,the numerical schemes developed in this research is hoped to bridge the gap between the evolution of numerical methods in ordinary differential equations(ODEs), delay differential equations (DDEs),stochastic differential equations(SDEs)and SDDEs.The extension of numerical methods of SDDEs is far from complete.Rate of convergence of recent numerical methods available in approximating the solution of SDDEs only reached the order of 1.0. …”
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Performance of 5-stage, 4-stage and specific stochastic Runge-Kutta methods in approximating the solution of stochastic biological model by Noor Amalina Nisa, Ariffin, Norhayati, Rosli, Abdul Rahman, Mohd Kasim, Mazma Syahidatul Ayuni, Mazlan

“…In recent years, the transition on modelling physical systems via stochastic differential equations (SDEs) has attracted great interest among researchers. …”
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Stochastic model of cancer growth with the effect of glycosaminoglycans (GAGs) as anticancer therapeutics by Mazma Syahidatul Ayuni, Mazlan

“…Ordinary differential equations (ODEs) and stochastic differential equations (SDEs) have been widely used to describe the biological process of cancer growth. …”
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Stochastic modelling of cancer cell proliferation and death in response to anticancer therapeutics of thymoquinone by Shabana, Tabassum

“…This research is aimed to formulate a system of stochastic differential equations (SDEs) for the apoptosis process in signalling pathways of cancer cell proliferation and death in response to TQ. …”
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