Lingai Guo¹, Marwan Fahs², Hussein Hoteit³, Rui Gao^1,*, Qian Shao^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 279-297, 2021, DOI:10.32604/cmes.2021.016619 - 24 August 2021

Abstract Numerical modeling of seepage-induced consolidation process usually encounters significant uncertainty in the properties of geotechnical materials. Assessing the effect of uncertain parameters on the performance variability of the seepage consolidation model is of critical importance to the simulation and tests of this process. To this end, the uncertainty and sensitivity analyses are performed on a seepage consolidation model in a fractured porous medium using the Bayesian sparse polynomial chaos expansion (SPCE) method. Five uncertain parameters including Young’s modulus, Poisson’s ratio, and the permeability of the porous matrix, the permeability within the fracture, and Biot’s constant… More >

Taekyun Kim^1,*, Dae San Kim², Dmitry V. Dolgy³, Si-Hyeon Lee¹, Jongkyum Kwon^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1121-1132, 2021, DOI:10.32604/cmes.2021.016532 - 11 August 2021

Abstract We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind. In this paper, we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials. We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates. More >

Naila Rafiq¹, Saima Akram², Mudassir Shams^3,*, Nazir Ahmad Mir¹

CMC-Computers, Materials & Continua, Vol.69, No.2, pp. 2635-2651, 2021, DOI:10.32604/cmc.2021.018955 - 21 July 2021

Abstract In this research article, we construct a family of derivative free simultaneous numerical schemes to approximate all real zero of non-linear polynomial equation. We make a comparative analysis of the newly constructed numerical schemes with a well-known existing simultaneous method for determining all the distinct real zeros of polynomial equations using computer algebra system Mat Lab. Lower bound of convergence of simultaneous schemes is calculated using Mathematica. Global convergence property of the numerical schemes is presented by taking random starting initial approximation and their convergence history are graphically presented. Some real life engineering applications along More >

Lu Li¹, Yuzhen Fan², Xinglang Su^1,*, Gefei Qiu¹

Energy Engineering, Vol.118, No.3, pp. 565-580, 2021, DOI:10.32604/EE.2021.014627 - 22 March 2021

Abstract Because of the randomness and uncertainty, integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow. This paper uses polynomial normal transformation method to deal with non-normal random variable correlation, and solves probabilistic load flow based on Kriging method. This method is a kind of smallest unbiased variance estimation method which estimates unknown information via employing a point within the confidence scope of weighted linear combination. Compared with traditional approaches which need a greater number of calculation times, long simulation time, and large memory space, Kriging More >

Park Chan-Yeob, Hyun-Ro Jae, Jun-Yong Jang, Song Hyoung-Kyu^*

CMC-Computers, Materials & Continua, Vol.68, No.1, pp. 137-148, 2021, DOI:10.32604/cmc.2021.016108 - 22 March 2021

Abstract Linear precoding methods such as zero-forcing (ZF) are near optimal for downlink massive multi-user multiple input multiple output (MIMO) systems due to their asymptotic channel property. However, as the number of users increases, the computational complexity of obtaining the inverse matrix of the gram matrix increases. For solving the computational complexity problem, this paper proposes an improved Jacobi (JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems. The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel… More >

W. M. Abd-Elhameed^1,2,*, Asmaa M. Alkenedri²

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 955-989, 2021, DOI:10.32604/cmes.2021.013603 - 19 February 2021

Abstract This paper is dedicated to implementing and presenting numerical algorithms for solving some linear and nonlinear even-order two-point boundary value problems. For this purpose, we establish new explicit formulas for the high-order derivatives of certain two classes of Jacobi polynomials in terms of their corresponding Jacobi polynomials. These two classes generalize the two celebrated non-symmetric classes of polynomials, namely, Chebyshev polynomials of third- and fourth-kinds. The idea of the derivation of such formulas is essentially based on making use of the power series representations and inversion formulas of these classes of polynomials. The derived formulas More >

Liqun Wang¹, Zengtao Chen², Guolai Yang^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 479-503, 2021, DOI:10.32604/cmes.2021.011954 - 21 January 2021

Abstract This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion (PCE). The uncertainty parameters with sufficient information are regarded as stochastic variables, whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge. In this method, the PCE model is constructed through the Galerkin projection method, in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights. Through the sampling in PCE, the original dynamic systems with hybrid stochastic and interval parameters can be transformed into… More >

Ali N. A. Koam¹, Ali Ahmad^{2, *}

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1271-1282, 2020, DOI:10.32604/cmc.2020.011736 - 20 August 2020

Abstract In order to study the behavior and interconnection of network devices, graphs structures are used to formulate the properties in terms of mathematical models. Mesh network (meshnet) is a LAN topology in which devices are connected either directly or through some intermediate devices. These terminating and intermediate devices are considered as vertices of graph whereas wired or wireless connections among these devices are shown as edges of graph. Topological indices are used to reflect structural property of graphs in form of one real number. This structural invariant has revolutionized the field of chemistry to identify 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 >

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 >