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 >

Ali Yousef^1,*, Fatma Bozkurt^1,2, Thabet Abdeljawad^3,4,5

CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 843-869, 2021, DOI:10.32604/cmc.2020.012060 - 30 October 2020

Abstract In this study, we classify the genera of COVID-19 and provide brief information about the root of the spread and the transmission from animal (natural host) to humans. We establish a model of fractional-order differential equations to discuss the spread of the infection from the natural host to the intermediate one, and from the intermediate one to the human host. At the same time, we focus on the potential spillover of bat-borne coronaviruses. We consider the local stability of the co-existing critical point of the model by using the Routh–Hurwitz Criteria. Moreover, we analyze the More >

Muhammad Shoaib Arif^1,*, Ali Raza^1,2, Kamaleldin Abodayeh³, Muhammad Rafiq⁴, Mairaj Bibi⁵, Amna Nazeer⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 477-491, 2020, DOI:10.32604/cmes.2020.011121 - 20 July 2020

Abstract The essential features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. The aim of our paper, to achieve the comparison analysis of the stochastic susceptible, infected recovered epidemic model. The stochastic modelling is a realistic way to study the dynamics of compartmental modelling as compared to deterministic modelling. The effect of reproduction number has also observed in the stochastic susceptible, infected recovered epidemic model. For comparison analysis, we developed some explicit stochastic techniques, but they are the More >

Gökçe Yıldız¹, Gültekin Tınaztepe^{2, *}, Mehmet Sezer¹

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 973-993, 2020, DOI:10.32604/cmes.2020.09329 - 28 May 2020

Abstract In this article, we approximate the solution of high order linear Fredholm integro-differential equations with a variable coefficient under the initial-boundary conditions by Bell polynomials. Using collocation points and treating the solution as a linear combination of Bell polynomials, the problem is reduced to linear system of equations whose unknown variables are Bell coefficients. The solution to this algebraic system determines the approximate solution. Error estimation of approximate solution is done. Some examples are provided to illustrate the performance of the method. The numerical results are compared with the collocation method based on Legendre polynomials More >

Marjan Uddin^{1, *}, Najeeb Ullah², Syed Inayat Ali Shah²

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 957-972, 2020, DOI:10.32604/cmes.2020.08911 - 28 May 2020

Abstract In this work, a numerical scheme is constructed for solving nonlinear parabolictype partial-integro differential equations. The proposed numerical scheme is based on radial basis functions which are local in nature like finite difference numerical schemes. The radial basis functions are used to approximate the derivatives involved and the integral is approximated by equal width integration rule. The resultant differentiation matrices are sparse in nature. After spatial approximation using RBF the partial integro-differential equations reduce to the system of ODEs. Then ODEs system can be solved by various types of ODE solvers. The proposed numerical scheme More >

An Chen^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 917-939, 2020, DOI:10.32604/cmes.2020.09224 - 28 May 2020

Abstract In this paper, two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered. These two models can be regarded as the generalization of the classical wave equation in two space dimensions. Combining with the Crank-Nicolson method in temporal direction, efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed, respectively. The corresponding stability and convergence analysis of the numerical methods are discussed. Numerical results are provided to verify the theoretical analysis. More >

M. H. T. Alshbool¹, W. Shatanawi^{2, 3, 4, *}, I. Hashim⁵, M. Sarr¹

CMC-Computers, Materials & Continua, Vol.64, No.1, pp. 63-80, 2020, DOI:10.32604/cmc.2020.09431 - 20 May 2020

Abstract One of the most attractive subjects in applied sciences is to obtain exact or approximate solutions for different types of linear and nonlinear systems. Systems of ordinary differential equations like systems of second-order boundary value problems (BVPs), Brusselator system and stiff system are significant in science and engineering. One of the most challenge problems in applied science is to construct methods to approximate solutions of such systems of differential equations which pose great challenges for numerical simulations. Bernstein polynomials method with residual correction procedure is used to treat those challenges. The aim of this paper… More >

Kazunori Shinohara^*

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 441-473, 2020, DOI:10.32604/cmes.2020.08656 - 01 May 2020

Abstract Addition formulas exist in trigonometric functions. Double-angle and half-angle formulas can be derived from these formulas. Moreover, the relation equation between the trigonometric function and the hyperbolic function can be derived using an imaginary number. The inverse hyperbolic function is similar to the inverse trigonometric function , such as the second degree of a polynomial and the constant term 1, except for the sign − and +. Such an analogy holds not only when the degree of the polynomial is 2, but also for higher degrees. As such, … More >

Mahdi Saedshoar Heris¹, Mohammad Javidi¹, Bashir Ahmad^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.1, pp. 249-272, 2019, DOI:10.32604/cmes.2019.08080

Abstract In this paper, we propose numerical methods for the Riesz space fractional advection-dispersion equations with delay (RFADED). We utilize the fractional backward differential formulas method of second order (FBDF2) and weighted shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and present the finite difference method for the RFADED. Firstly, the FBDF2 and the shifted Grünwald methods are introduced. Secondly, based on the FBDF2 method and the WSGD operators, the finite difference method is applied to the problem. We also show that our numerical schemes are conditionally stable and convergent with the accuracy More >

Kazunori Shinohara^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.3, pp. 599-647, 2019, DOI:10.31614/cmes.2019.04472

Abstract According to the wave power rule, the second derivative of a function x(t) with respect to the variable t is equal to negative n times the function x(t) raised to the power of 2n-1. Solving the ordinary differential equations numerically results in waves appearing in the figures. The ordinary differential equation is very simple; however, waves, including the regular amplitude and period, are drawn in the figure. In this study, the function for obtaining the wave is called the leaf function. Based on the leaf function, the exact solutions for the undamped and unforced Duffing equations… More >