Haolun Zhang¹, Mengna Yang¹, Jie Wei², Yufeng Nie^2,*

Digital Engineering and Digital Twin, Vol.2, pp. 49-77, 2024, DOI:10.32604/dedt.2023.044180

Abstract This paper mainly considers the formulation and theoretical analysis of the reduced-order numerical method constructed by proper orthogonal decomposition (POD) for nonlocal diffusion problems with a finite range of nonlocal interactions. We first set up the classical finite element discretization for nonlocal diffusion equations and briefly explain the difference between nonlocal and partial differential equations (PDEs). Nonlocal models have to handle double integrals when using finite element methods (FEMs), which causes the generation of algebraic systems to be more challenging and time-consuming, and discrete systems have less sparsity than those for PDEs. So we establish a reduced-order model (ROM) for… More >

Rongge Xiao^a , Yue Zhu^b,*, Wenbo Jin^a , Zheng Dai^a , Shifang Li^a , Fan Zhang^c

Frontiers in Heat and Mass Transfer, Vol.12, pp. 1-6, 2019, DOI:10.5098/hmt.12.28

Abstract In order to accurately obtain the wax deposition rate model, according to the kinetic principle of wax deposition, several factors affecting the wax deposition rate were selected, and by a optimization software of First Optimization(1stOpt), The parameters of two typical wax deposition rate models are solved respectively based on optimization algorithm combined by Levenberg-Marquardt (L-M) algorithm and global optimization and the calculated data were compared. The results show that: compared with the model parameters obtained by least squares method, the model parameters obtained by this optimization algorithm can describe the variation of wax deposition rate more accurately. The maximum error… More >

C. Thiruvengadam^1,*, M. Palanivelan²

Intelligent Automation & Soft Computing, Vol.36, No.3, pp. 2803-2818, 2023, DOI:10.32604/iasc.2023.030493

Abstract There are numerous goals in next-generation cellular networks (5G), which is expected to be available soon. They want to increase data rates, reduce end-to-end latencies, and improve end-user service quality. Modern networks need to change because there has been a significant rise in the number of base stations required to meet these needs and put the operators’ low-cost constraints to the test. Because it can withstand interference from other wireless networks, and Adaptive Complex Multicarrier Modulation (ACMM) system is being looked at as a possible choice for the 5th Generation (5G) of wireless networks. Many arithmetic units need to be… More >

Radwan Abu-Gdairi¹, Shatha Hasan², Shrideh Al-Omari^3,*, Mohammad Al-Smadi^2,4, Shaher Momani^4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 299-313, 2022, DOI:10.32604/cmes.2022.017010

Abstract In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform form for a rapidly convergent series in the posed Sobolev space. Using the Gram-Schmidt orthogonality process, complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction. Consequently, by applying the standard RKHS method to each subinterval, approximate solutions that converge uniformly to the exact solutions are obtained. For this purpose,… More >

Cang Peng¹, Yu Zhenglin²

Intelligent Automation & Soft Computing, Vol.25, No.4, pp. 827-835, 2019, DOI:10.31209/2019.100000086

Abstract The assembly error of the supporting component in Mobile Lidar has an inevitable influence on the positioning accuracy and the system error. In this paper, we applied the multi-body system kinematics principle and the homogeneous coordinate transformation to infer the final pointing error formula which influences the three-axis error model of the Mobile Lidar. The influence of each error item on the positioning accuracy (pointing accuracy) of radar system is analyzed by computer simulation, and the motion law between each axis of radar supporting component is discussed, which has laid the base for researching the positioning accuracy of Mobile Lidar. More >

Bo Xiao¹, Yinghang Jiang², Qi Liu^{2, 5, *}, Xiaodong Liu³, Mingxu Sun^{4, *}

CMC-Computers, Materials & Continua, Vol.64, No.1, pp. 389-399, 2020, DOI:10.32604/cmc.2020.06092

Abstract MEMS accelerometers are widely used in various fields due to their small size and low cost, and have good application prospects. However, the low accuracy limits its range of applications. To ensure data accuracy and safety we need to calibrate MEMS accelerometers. Many authors have improved accelerometer accuracy by calculating calibration parameters, and a large number of published calibration methods have been confusing. In this context, this paper introduces these techniques and methods, analyzes and summarizes the main error models and calibration procedures, and provides useful suggestions. Finally, the content of the accelerometer calibration method needs to be overcome. More >

W. M. Abd- Elhameed^1,2, Y. H. Youssri²

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.5, pp. 375-398, 2015, DOI:10.3970/cmes.2015.105.375

Abstract In this paper, a new spectral algorithm for solving linear and nonlinear fractional-order initial value problems is established. The key idea for obtaining the suggested spectral numerical solutions for these equations is actually based on utilizing the ultraspherical wavelets along with applying the collocation method to reduce the fractional differential equation with its initial conditions into a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. The convergence and error analysis of the suggested ultraspherical wavelets expansion are carefully discussed. For the sake of testing the proposed algorithm, some numerical examples are considered. The numerical results indicate… More >

Baofeng Li ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 105-122, 2014, DOI:10.3970/cmes.2014.099.105

Abstract In this paper, operational matrix method based on the generalized hat functions is introduced for the approximate solutions of linear and nonlinear fractional integro-differential equations. The fractional order generalized hat functions operational matrix of integration is also introduced. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations. In addition, the method is presented with error analysis. Numerical examples are included to demonstrate the validity and applicability of the approach. More >

Lifeng Wang¹, Yunpeng Ma^1,2, Yongqiang Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 97-111, 2014, DOI:10.3970/cmes.2014.101.097

Abstract In this paper, a numerical method based on the Legendre polynomials is presented for a class of variable order fractional differential equation. We adopt the Coimbra variable order fractional operator, which can be viewed as a Caputo-type definition. Three different kinds of operational matrixes with Legendre polynomials are derived. A truncated the Legendre polynomials series together with the products of several dependent matrixes are utilized to reduce the variable order fractional differential equation to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited n. An error analysis technique is also given.… More >

Yunpeng Ma¹, Lifeng Wang¹, Zhijun Meng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.1, pp. 31-47, 2013, DOI:10.3970/cmes.2013.096.031

Abstract In this paper, we propose a numerical algorithm for solving linear and nonlinear fractional integro-differential equations based on our constructed fractional order generalized block pulse functions operational matrix of integration. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations by the matrix and these algebraic equations are solved through known computational methods. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach. Moreover, comparing the methodology with the known technique shows that our approach is more efficient and more convenient. More >