Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Muhammad Rafiq⁶, Mairaj Bibi⁷, Muhammad Mohsin⁸

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 201-215, 2021, DOI:10.32604/cmes.2021.012111 - 22 December 2020

Abstract Nonlinear stochastic modelling plays an important character in the different fields of sciences such as environmental, material, engineering, chemistry, physics, biomedical engineering, and many more. In the current study, we studied the computational dynamics of the stochastic dengue model with the real material of the model. Positivity, boundedness, and dynamical consistency are essential features of stochastic modelling. Our focus is to design the computational method which preserves essential features of the model. The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature. Analysis and comparison were explored in More >

Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Kamaledin Abodayeh¹, Muhammad Rafiq⁶, Mairaj Bibi⁷

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1121-1137, 2021, DOI:10.32604/cmc.2020.012070 - 26 November 2020

Abstract Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined More >