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- MakaleAçık Erişim2023Scopus SJRQ4Wong-Zakai approximation for stochastic models of smoking
Şengül, Süleyman; Beki̇Ryazici, Zafer; Merdan, Mehmet
In this study, Wong-Zakai approximation method has been used to obtain approximate solutions for two compartmental models of smoking dynamics. Stratonovich stochastic differential equation systems are obtained for these two stochastic models for the application of Wong-Zakai method. Wong-Zakai method is used together with the predictor-corrector deterministic approximation method where Adams-Bashforth method is used as the predictor pair and Adams-Moulton method is used as the corrector pair. Stochastic Runge-Kutta IV, Euler-Maruyama and stochastic Runge-Kutta strong order 1.0 schemes are also used to investigate the models and the results are compared to the results from Wong-Zakai approximation. The comparison shows that Wong-Zakai method is a reliable tool for the analysis of stochastic models and can be considered as an alternative investigation method for modeling studies. Solution graphs, error graphs and numerical results have been given as evidence to show that Wong-Zakai method can also be a reliable method for analyzing various models. An alternate technique for parallelizing the algorithm has also been given to decrease CPU times for Wong-Zakai method. This technique is suggested to overcome the extra calculation load that comes with Wong-Zakai method.
AtıfScopus2WoS2İncele - MakaleAçık Erişim2021Scopus SJRQ3Wong-Zakai Method for Stochastic Differential Equations in Engineering
Sengul, Suleyman; Bekiryazici, Zafer; Merdan, Mehmet
In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Maruyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can be used as an alternative for the known approximation techniques for stochastic models.
AtıfScopus4WoS4OpenAlex5İncele - MakaleAçık Erişim2017Scopus SJRQ2Comparison of stochastic and random models for bacterial resistance
Merdan, Mehmet; Bekiryazici, Zafer; Kesemen, Tulay; Khaniyev, Tahir
In this study, a mathematical model of bacterial resistance considering the immune system response and antibiotic therapy is examined under random conditions. A random model consisting of random differential equations is obtained by using the existing deterministic model. Similarly, stochastic effect terms are added to the deterministic model to form a stochastic model consisting of stochastic differential equations. The results from the random and stochastic models are also compared with the results of the deterministic model to investigate the behavior of the model components under random conditions.
AtıfScopus25WoS25OpenAlex25İncele