Vibration of a Cylindrical Tunnel under a Centric Point-Source Explosion by Yuetang Zhao, Cheng Chu, Anastasios Vafeidis, Jie Li

“…The governing equation of the motion is a fourth-order partial differential equation, for which a numerical method combining finite difference with the implicit Newmark-β method was adopted. …”
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Experimental and Numerical Investigations of Pressure Field of Curved Shell Structure Subjected to Interior Blast by Jialu Ma, Feng Fan, Lingxin Zhang, Chengqing Wu, Xudong Zhi

“…A parametrical analysis of the interior blast simulations was conducted based on this numerical method. The blast loading values at specific positions were obtained with the key parameters varied within a reasonable scope. …”
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A Parametric Design Method for Hybrid Airfoils for Icing Wind Tunnel Test by Zhao Li, Guang-jun Yang, Xiao-yan Tong, Feng Jiang

“…Finally, the vortex distribution and ice accretion process of the two airfoils were simulated by the unsteady Reynolds-averaged-Navier–Stokes (URANS) equations and multistep ice numerical method; it is shown that the hybrid airfoil can provide the same vortex distribution and ice accretion with the full-scale airfoil.…”
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Numerical Solutions of Duffing Van der Pol Equations on the Basis of Hybrid Functions by M. Mohammadi, A. R. Vahidi, T. Damercheli, S. Khezerloo

“…The main goal of the presented technique is to transform these problems into a nonlinear system of algebraic equations using the operational matrix obtained from the integration, which can be solved by a proper numerical method; thus, the solution procedures are either reduced or simplified accordingly. …”
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Characterization of Contact-Type Defects in Mortar Using a Nonlinear Ultrasonic Method by Zhichao Nie, Kui Wang, Mingjie Zhao, Xiao Sun

“…For this purpose, by the numerical method, the contact interface in mortar is characterized based on the damage indicator γ. …”
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Compact scheme with two-sided estimates for nonlinear convection-diffusion-reaction equations by Chinedu Nwaigwe

“… It is desirable that a numerical method is high-order accurate, compact, efficient and able to simulate purely convection problems. …”
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Size-Dependent Dynamic Behavior of Axially Moving Graphene Nanosheets Using Nonlocal First-Order Shear Deformation Theory by Huafeng Tian

“…Using Hamilton's principle, nonlinear equations governing motion are extracted and then discretized using the Galerkin method. Based on the numerical method, the dynamic response and vibration characteristics of these systems are determined. …”
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Urban Lead: Modeling Its Distribution and Effects on Children by Zhixiong Chen, Yi Ding, Andrew Getz, Bernard Lipat

“…The model is solved using the Crank-Nicolson numerical method at the macroscale to determine the deposition of lead from the smelting plant and the local power plant and at the mesoscale to refine the amount of lead deposition for the areas considered. …”
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Bi-Threshold Cooperative Spectrum Sensing With the Ability of Simultaneous Improving Throughput and Reducing Energy Consumption in Cognitive Radio Network by Masoud Moradkhani, Farzad Soltanian

“…The optimization problem is formulated and a numerical method is presented to solve it. The simulation results show a flexible system that can simultaneously provide higher throughput and lower energy consumption than the conventional sensing method. …”
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Influence of the Eccentric Error of Star Gear on the Bifurcation Properties of Herringbone Star Gear Transmission with Floating Sun Gear by Fang Guo, Zongde Fang, Xijin Zhang, Yanmei Cui

“…For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time-varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. …”
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A Unique Finite Element Modeling of the Periodic Wave Transformation over Sloping and Barred Beaches by Beji and Nadaoka's Extended Boussinesq Equations by Mohammad Hadi Jabbari, Parviz Ghadimi, Mesbah Sayehbani, Arsham Reisinezhad

“…Stability of the suggested numerical method is also analyzed. Subsequently, in order to display the ability of the presented model, four different test cases are considered. …”
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Evaluasi Frame Sepeda saat Tabrakan Dengan Metode Ekplisit Elemen Hingga by Ardi Wiranata, Abdul Arief, Heru Santoso Budi Rochardjo

“…In this paper, numerical method of crash impact by using explicit dynamic model was used to evaluate the bike frame design. …”
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Comparison Between Newton's Interpolation and Lagrange Method with Runge Kutt a Method in Solving First Order Differential Equations. by Muligi, Amos

“…The result showed that a combination of Newton's interpolation and Lagrange method gives a small absolute error and therefore efficient method for solving first-order differential equations. The numerical method used (Runge Kutta) is cumbersome and has a bigger percentage error. …”
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Study on the Effect of Amygdales on Mechanical Characteristics of Basalt Using the Combined Finite-Discrete Element Method by Shirui Zhang, Shili Qiu, Ping Li, Yongyuan Kou, Pengfei Kou

“…This paper provides a numerical method for studying the mechanical properties of rocks with flaws.…”
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Study on Relaxation Damage Properties of High Viscosity Asphalt Sand under Uniaxial Compression by Yazhen Sun, Zhangyi Gu, Jinchang Wang, Chenze Fang, Xuezhong Yuan

“…Results show that the numerical method of coupling damage provides a better approximation of the test curve over almost the whole range. …”
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Modeling the Hydrodynamic Pressure Field and Wake Field Characteristics of an Underwater Vehicle and Studying Their Correlation by Peihao Li, Hui Deng, Bingrui Xu, Weixue Xia, Wenbin Yi

“…In this paper, a numerical method is established based on the Reynolds-averaged Navier–Stokes equation. …”
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Numerical Simulations of Chemical-Assisted Steam Flooding in Offshore Heavy Oil Reservoirs after Water Flooding by Wei Zheng, Tingen Fan, Xianhong Tan, Weidong Jiang, Taichao Wang, Haojun Xie

“…The results showed that the developed numerical method can precisely simulate the CASF processes. …”
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Numerical research on the influence of ventilation velocity on fire smoke distribution in bifurcated roadway by Cui DING

“…In order to investigate the influence of ventilation velocity on fire smoke distribution in bifurcated roadway, the computational fluid dynamics (CFD) numerical method was adopted to simulate the fires located in upstream of main-roadway. …”
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Assessment of Bioprocess Development-Based Modeling and Simulation in a Sustainable Environment by R. Satish Kumar, B. Nageswara Rao, M. Prameela, S. Peniel Pauldoss, Amol L. Mangrulkar, Saleh H. Salmen, Sami Al Obaid, S. Sappireamaniyan, Kibrom Menasbo Hadish

“…A valuable commitment to sustainability bioprocess modeling and evaluation can be made by using a first-approximation numerical method as the basis for financial and environmental evaluations.…”
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Finite volume modeling of neural communication: Exploring electrical signaling in biological systems by Muzammal Saleem, Muhammad Saqib, Badar Saad Alshammari, Shahid Hasnain, Amjad Ayesha

“…Validation through comparison with existing literature and computational simulations demonstrates strong agreement between predicted outcomes and those generated by the model. The numerical method proves to be a reliable and precise tool for modeling the dynamics of physical systems, with potential applications in fields such as electromagnetism, acoustics, and fluid mechanics.…”
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