Zulqurnain Sabir¹, Muhammad Umar¹, Muhammad Asif Zahoor Raja^2,*, Dumitru Baleanu^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 227-251, 2021, DOI:10.32604/cmes.2021.016611

Abstract The presented research aims to design a new prevention class (P) in the HIV nonlinear system, i.e., the HIPV model. Then numerical treatment of the newly formulated HIPV model is portrayed handled by using the strength of stochastic procedure based numerical computing schemes exploiting the artificial neural networks (ANNs) modeling legacy together with the optimization competence of the hybrid of global and local search schemes via genetic algorithms (GAs) and active-set approach (ASA), i.e., GA-ASA. The optimization performances through GA-ASA are accessed by presenting an error-based fitness function designed for all the classes of the HIPV model and its corresponding… More >

Mohd Ahmed^1,*, Devender Singh², Saeed Al Qadhi¹, Nguyen Viet Thanh³

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 167-189, 2021, DOI:10.32604/cmes.2021.014672

Abstract The performance of a-posteriori error methodology based on moving least squares (MLS) interpolation is explored in this paper by varying the finite element error recovery parameters, namely recovery points and field variable derivatives recovery. The MLS interpolation based recovery technique uses the weighted least squares method on top of the finite element method's field variable derivatives solution to build a continuous field variable derivatives approximation. The boundary of the node support (mesh free patch of influenced nodes within a determined distance) is taken as circular, i.e., circular support domain constructed using radial weights is considered. The field variable derivatives (stress… More >

Pinjie Xie^1,*, Ying Zhai¹, Fan Yang^1,2, Zhuowen Mu³, Chao Wang⁴

Energy Engineering, Vol.118, No.5, pp. 1353-1374, 2021, DOI:10.32604/EE.2021.014970

Abstract Electricity productivity is regarded as a major assessment indicator in the design of energy saving policies, given that China has entered a “New Normal” of economic development. In fact, enhancing electricity productivity in an all-round way, as is one of the binding indicators for energy and environmental issues, means that non-growth target of total electric energy consumption in the economic development is feasible. The Gini coefficient, Theil index, and Mean log deviation are utilized to measure regional differences in China’s electricity productivity from 1997 to 2016 in five regions, and conditional β convergence is empirically analyzed with the spatial Durbin… More >

I. G. Ameen¹, N. A. Elkot², M. A. Zaky^3,*, A. S. Hendy^4,5, E. H. Doha²

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.1, pp. 21-41, 2021, DOI:10.32604/cmes.2021.015310

Abstract We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left- and right-sided fractional derivatives. The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations. Then, a Legendre-based spectral collocation method is developed for solving the transformed system. Therefore, we can make good use of the advantages of the Gauss quadrature rule. We present the construction and analysis of the collocation method. These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange equations. Two numerical examples… More >

Ali. F. Jameel^1,*, N. R. Anakira², A. K. Alomari³, Noraziah H. Man¹

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 875-899, 2021, DOI:10.32604/cmes.2021.014460

Abstract Homotopy Analysis Method (HAM) is semi-analytic method to solve the linear and nonlinear mathematical models which can be used to obtain the approximate solution. The HAM includes an auxiliary parameter, which is an efficient way to examine and analyze the accuracy of linear and nonlinear problems. The main aim of this work is to explore the approximate solutions of fuzzy Volterra integral equations (both linear and nonlinear) with a separable kernel via HAM. This method provides a reliable way to ensure the convergence of the approximation series. A new general form of HAM is presented and analyzed in the fuzzy… More >

Muhammad Amin¹, Muhammad Abbas^2,*, Dumitru Baleanu^3,4,5, Muhammad Kashif Iqbal⁶, Muhammad Bilal Riaz⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 361-384, 2021, DOI:10.32604/cmes.2021.012720

Abstract This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes… More >

Mustafa Turkyilmazoglu^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 1-22, 2021, DOI:10.32604/cmes.2021.012595

Abstract The present paper is devoted to the convergence control and accelerating the traditional Decomposition Method of Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding a parameterized term, containing an embedded parameter, new modified ADM is constructed. The optimal value of this parameter is later determined via squared residual minimizing the error. The failure of the classical ADM is also prevented by a suitable value of the embedded parameter, particularly beneficial for the Duan–Rach modification of the ADM incorporating all the boundaries into the formulation. With the presented squared residual error analysis,… More >

Ali Mustafa^1,2, M Najam ul Islam¹, Salman Ahmed^1,3,*

Computer Systems Science and Engineering, Vol.37, No.3, pp. 399-413, 2021, DOI:10.32604/csse.2021.015575

Abstract Consensus control of multi-agent systems is an innovative paradigm for the development of intelligent distributed systems. This has fascinated numerous scientific groups for their promising applications as they have the freedom to achieve their local and global goals and make their own decisions. Network communication topologies based on graph and matrix theory are widely used in a various real-time applications ranging from software agents to robotics. Therefore, while sustaining the significance of both directed and undirected graphs, this research emphases on the demonstration of a distributed average consensus algorithm. It uses the harmonic mean in the domain of multi-agent systems… 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

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 serve in converting the even-order… More >

Obadah Said Solaiman¹, Samsul Ariffin Abdul Karim², Ishak Hashim^1,*

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 1951-1962, 2021, DOI:10.32604/cmc.2021.015344

Abstract There are several ways that can be used to classify or compare iterative methods for nonlinear equations, for instance; order of convergence, informational efficiency, and efficiency index. In this work, we use another way, namely the basins of attraction of the method. The purpose of this study is to compare several iterative schemes for nonlinear equations. All the selected schemes are of the third-order of convergence and most of them have the same efficiency index. The comparison depends on the basins of attraction of the iterative techniques when applied on several polynomials of different degrees. As a comparison, we determine… More >