Shumaila Azam¹, Nauman Ahmed^1,6, Ali Raza², Muhammad Sajid Iqbal¹, Muhammad Rafiq³, Ilyas Khan^4,*, Kottakkaran Sooppy Nisar⁵, Muhammad Ozair Ahmad¹, Zafar Iqbal^1,6

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2933-2953, 2021, DOI:10.32604/cmc.2021.012396

Abstract Recently, the world is facing the terror of the novel corona-virus, termed as COVID-19. Various health institutes and researchers are continuously striving to control this pandemic. In this article, the SEIAR (susceptible, exposed, infected, symptomatically infected, asymptomatically infected and recovered) infection model of COVID-19 with a constant rate of advection is studied for the disease propagation. A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system. The continuous model is transposed into a discrete numerical model by discretizing the domains, finitely. To analyze the disease dynamics,… More >

Naveed Shahid^1,2, Dumitru Baleanu^3,4,5, Nauman Ahmed^1,2, Tahira Sumbal Shaikh⁶, Ali Raza^7,*, Muhammad Sajid Iqbal¹, Muhammad Rafiq⁸, Muhammad Aziz-ur Rehman²

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1713-1728, 2021, DOI:10.32604/cmc.2021.014191

Abstract The novel coronavirus disease, coined as COVID-19, is a murderous and infectious disease initiated from Wuhan, China. This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far. In this article, the spatio-temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed. To counteract these types of diseases or restrict their spread, mankind depends upon mathematical modeling and medicine to reduce, alleviate, and anticipate the behavior of disease dynamics. The existence and uniqueness of the solution for the proposed system are investigated.… 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 of O(k+ h²) and O(k²… More >

Sitta Aroonnual Paisan Kanthang, Wannapong Triampo¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.13, No.3, pp. 53-54, 2009, DOI:10.3970/icces.2009.013.053

Abstract How does a cell successfully divide is one of very fundamental questions in biological and medical science especially concerning mechanism. With this regards, MinE proteins are very important for Escherichia coli cell division process because it supports FtsZ proteins to form at mid-cell which lead to cell division at that region. In this work, we quantitatively studied the physical properties of MinE protein clusters including pattern formations and dynamic motions using both theoretical and experimental approach. Experimentally, through the spot tracking technique (STT) and diffusion analysis, it was found that MinE globally performed oscillatory motion from middle cell to the… More >

Xia Yuan¹, Wu Jichun², Zhou Luying³

The International Conference on Computational & Experimental Engineering and Sciences, Vol.9, No.2, pp. 117-126, 2009, DOI:10.3970/icces.2009.009.117

Abstract This paper establishes a difference approximation on time-space fractional advection-dispersion equations. Based on the difference approximation an ideal numerical example has been solved, and the result is compared with the one of the rigorous time fractional advection-dispersion equation and the rigorous space fractional advection-dispersion equation respectively. The results show: when time fractional order parameter γ=1 or space fractional order parameter α=2, the numerical calculation result of the time-space fractional advection-dispersion equations is in accordance with that of the rigorous time fractional advection-dispersion equation or the rigorous space fractional advection-dispersion equation. The variation law of the result with parameter is also… More >

Guofei Pang¹, Wen Chen^1,2, K.Y. Sze³

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.4, pp. 299-322, 2014, DOI:10.3970/cmes.2014.097.299

Abstract Space-fractional advection-diffusion equation is a promising tool to describe the solute anomalous transport in underground water, and it has been extended to multi-dimensions with the help of weighted, fractional directional diffusion operator [Benson, Wheatcraft and Meerschaert (2000)]. Due to the nonlocal property of the space-fractional derivative, it is always a challenge to develop an efficient numerical solution method. The present paper extends the polynomialbased differential quadrature and cubature methods to the solution of steady-state spatial fractional advection-diffusion equations on a rectangular domain. An improved differential cubature method is proposed which accelerates the solution process considerably. Owing to the global interpolation… More >

Hui Wei^1,2,3, Wen Chen^1,2,4, HongGuang Sun^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.2, pp. 85-103, 2014, DOI:10.3970/cmes.2014.100.085

Abstract The unknown parameters are critical factors in fractional derivative advection-dispersion equation describing the solute transport in soil. For examples, the fractional derivative order is the index of anomalous dispersion, diffusion coefficient represents the dispersion ability of media and average pore-water velocity denotes the main trend of transport, etc. This paper is to develop a homotopy method to determine the unknown parameters of solute transport with spatial fractional derivative advection-dispersion equation in soil. The homotopy method can be easily developed to solve parameter determination problems of fractional derivative equations whose analytical solutions are difficult to obtain. The sigmoid function is involved… More >

E. Tombarević¹, V. R. Voller², I. Vušanović¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.1, pp. 1-29, 2013, DOI:10.3970/cmes.2013.096.001

Abstract The Control Volume Finite Element Method (CVFEM) combines the geometric flexibility of the Finite Element Method (FEM) with the physical intuition of the Control Volume Method (CVM). These two features of the CVFEM make it a very powerful tool for solving heat and fluid flow problems within complex domain geometries. In solving problems in the two-dimensional domains the development of the CVFEM has been well documented. For the three-dimensional problems, while there is extensive reporting on the details of the numerical approximation, there is relatively sparse information on important issues related to data structure and interpolation. Here, in the context… More >

Chih-Wen Chang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.2, pp. 65-92, 2012, DOI:10.3970/cmes.2012.088.065

Abstract We utilize a regularized integral equation scheme to resolve the three-dimensional backward advection-dispersion equation (BADE) for identifying the groundwater pollution source identification problems in this research. First, the Fourier series expansion method is employed to estimate the concentration field C(x, y, z, t) at any time t < T. Second, we contemplate a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for C(x, y, z, 0). The termwise separable property of the kernel function permits us to acquire a closed-form regularized solution. In addition, a tactic to determine the regularization… More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 261-276, 2009, DOI:10.3970/cmes.2009.051.261

Abstract The backward advection-dispersion equation (ADE) for identifying the groundwater pollution source identification problems (GPSIPs) is numerically solved by employing a fictitious time integration method (FTIM). The backward ADE is renowned as ill-posed because the solution does not continuously count on the data. We transform the original parabolic equation into another parabolic type evolution equation by introducing a fictitious time coordinate, and adding a viscous damping coefficient to enhance the stability of numerical integration of the discretized equations by employing a group preserving scheme. When several numerical examples are amenable, we find that the FTIM is applicable to retrieve all past… More >