Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations by S. Bivani, M. Ghasemi, A. Goligerdian

“…Abstract A numerical method based on fractional B-spline is developed and examined to approximate the solution of fractional multiterm pantograph equations. …”
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Multipotential Surface Elastoplastic Constitutive Model and Its Application in the Analysis of the Phase II Cofferdam of the Three Gorges Project by Yong Wen, Guanghua Yang, Zhihui Zhong

“…In addition, the proposed model uses a numerical method to fit the test curves to determine the required parameters. …”
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On the Solutions of Fractional Burgers-Fisher and Generalized Fisher’s Equations Using Two Reliable Methods by A. K. Gupta, S. Saha Ray

“…Haar wavelet method is an efficient numerical method for the numerical solution of arbitrary order partial differential equations like Burgers-Fisher and generalized Fisher equations. …”
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A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations by Xiaomin Wang

“…Thus, one can obtain a stable, highly accurate, and efficient numerical method without calculating the connection coefficients in traditional Galerkin method for solving the nonlinear algebraic equations. …”
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Numerical Simulation of Nonlinear Oil Film Forces of Tilting-Pad Guide Bearing in Large Hydro-unit by Li-Feng Ma, Xin-Zhi Zhang

“…A new numerical method is proposed for predicting the nonlinearity of tilting-pad guide bearing oilfilm force in the rotor-bearing system in a large hydro-unit. …”
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Applying Finite Element Method–Dirichlet Boundary Condition Iteration to the Computation of Coupling Factors for a 3-D Human Model by Giovanni Aiello, Salvatore Alfonzetti, Santi Agatino Rizzo, Nunzio Salerno

“…The hybrid FEM-DBCI numerical method is proposed for the computation of coupling factors between time-harmonic magnetic fields and human bodies. …”
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The Numerical Simulation Method of the Slot Crack Groups’ Effect Analysis for Solid Rocket Motor Grain by Tianpeng Li, Xiaonan Li, Zhaolong Xuan, Yu Guo

“…Moreover, the experimental result showed that the numerical method had high accuracy.…”
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Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions by Fukang Yin, Junqiang Song, Yongwen Wu, Lilun Zhang

“…A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). …”
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EXPERIMENTAL AND NUMERICAL STUDY OF A VENTURI TUBE AS A DIDACTIC TOOL FOR CHEMICAL ENGINEERING LEARNING by Felipe Orlando da Costa, Jéssica Trindade Martins, Caio Guilherme Sales Ferreira, Giovanna Kellen Tavares de Andrade, Felipe Leonardo Barcelos Mateus, Renata de Aquino Brito Lima Corrêa

“…The discharge coefficient was 0.680 ± 0.018 [-], an intermediate value of those found in the literature for orifice plate and flow nozzle meters. The numerical method was successfully able to predict the pressure drop in the system. …”
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Nonlinear Dynamical Analysis for the Cable Excited with Parametric and Forced Excitation by C. Z. Qian, C. P. Chen, G. W. Zhou

“…At last, by means of numerical method and software MATHMATIC, the effect rules of system parameters to the dynamical behavior of the system are studied, and some useful conclusions are obtained.…”
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A Mesoscale Approach for Concrete Block Masonry by Xu Yang, Mingming Jia, Bin Chi, Mingzhi Wang, Jianfeng Zheng

“…A comprehensive understanding of the concrete block masonry’s mesostructure on its macroscopic mechanical behavior is meaningful for modern masonry. The mesoscale numerical method provides an extremely powerful analyzing tool for this problem. …”
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A hybrid model for traffic flow and crowd dynamics with random individual properties by Veronika Schleper

“…The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models.…”
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On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications by Teng-fei Li, Heng-you Lan

“…In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature, and to analyze the convergence and stability of the proposed method. …”
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Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation by Jing-Jing Zhang, Xiang-Gui Li, Jing-Fang Shao

“…A high-order accuracy numerical method is proposed to solve the (1+1)-dimensional nonlinear Dirac equation in this work. …”
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Convergence Analysis Hilbert Space Approach for Fuzzy Integro-Differential Models by Jingwen Zhang

“…In this paper, we present and demonstrate an innovative numerical method, which makes use of fuzzy numbers and fuzzy parameters that is effective in the solution of fuzzy type Volterra integro-differential equations, which was previously thought to be impossible using conventional methods. …”
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Influence of Segmented Linings on the Micro-Pressure Wave of Tunnels by Tao Li, Mingyu Shao, Weibin Ma, Yanbin Liang, Yufei Fang

“…In this study, a three-dimensional numerical method is performed to study the aerodynamic effects caused by the train passing through a tunnel with segmented linings at 350 km/h. …”
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Fixation Probabilities on Complete Star and Bipartite Digraphs by Chunming Zhang, Yingjiang Wu, Wanping Liu, Xiaofan Yang

“…By applying these probability formulae, some asymptotic properties on CBDs are analyzed, and certain CSDs are determined to be amplifiers of selection for arbitrary relative fitness larger than 1, while all the CSDs are proved to be amplifiers of selection for fixed relative fitness slightly larger than 1. A numerical method for fixed population structure (by solving a linear system) is developed to calculate the fixation probabilities on complete bipartite digraphs (CBDs), and some conjectures are finally given through simulations.…”
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Bow Flare Water Entry Impact Prediction and Simulation Based on Moving Particle Semi-Implicit Turbulence Method by Fenglei Han, Jingzheng Yao, Chunhui Wang, Haitao Zhu

“…Prandtl’s mixing length method and the k-epsilon method are introduced into the Moving Particle Semi-Implicit (MPS) method for the purpose of modeling turbulence effects associated with water entries of two-dimensional (2D) bow flare section. The presented numerical method is validated by comparing its numerical prediction with experimental data and other numerical results obtained from the Boundary Element Method (BEM). …”
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Unsteady free convection of a stagnation point of attachment on an isothermal surface by D. B. Ingham, J. H. Merkin, I. Pop

“…A small time solution and an accurate numerical method is described for determining the solution of the time-dependent boundary-layer equations. …”
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Holographic Schwinger Effect in a Confining D3-Brane Background with Chemical Potential by Zi-qiang Zhang, De-fu Hou, Yan Wu, Gang Chen

“…The critical field Ec in this case is calculated. Also, we apply numerical method to evaluate the production rate for various cases. …”
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