Finite Element Analysis for Estimating Strength and Fatigue of the APM Structure by Klabklay Teerawat, Sumpavakup Chaiyut, Khumkrong Asawadech, Thasanavirud Natthikan, Pensuk Pannachai

“…The grid independence test, which is a significant process in numerical method, is carried out. The results show that the maximum displacements of the chassis, floor, body, roof, and support provide 13.3, 1.13, 0.21, 2.0, and 0.06 millimeters, respectively. …”
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Water quality model-based methodology to assess assimilative capacity of wastewater discharges in rivers by F.M. Torres-Bejarano, M. Verbel-Escobar, M.C. Atencia-Osorio

“…BACKGROUND AND OBJECTIVES: One of the negative impacts of polluting activities on aquatic ecosystems is the loss of its natural self-purification ability, for this reason, the purpose of this research was to evaluate the Sinú river capacity to assimilate wastewater discharges.METHODS: Monitoring of several water quality parameters was carried out in the river at different seasons and a numerical method was used to simulate different scenarios through the Environmental Fluid Dynamics Code model. …”
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Investigation of Heat and Mass Transfer in the Process of Fuel Preparation from Biomass Particles with High Moisture by A. V. Mitrofanov, O. B. Kolibaba, R. N. Gabitov, D. A. Dolinin, S. V. Vasilevich

“…In the course of the study, the following tasks were solved: a numerical method was developed for describing the processes of internal and external heat and mass transfer problems using an explicit difference approximation of differential equations of heat and mass transfer; parametric identification of the proposed one-dimensional mathematical model was performed using empirical dependencies known from literature sources; empirical verification of the proposed mathematical model was carried out by comparing the calculated forecasts obtained with the results of their own field experiments. …”
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New Leakage Model for Naturally Fractured Formations Considering the Effects of Dual-System Hydro-Mechanical Coupling by Hao Peng, Qian Li, JiaJia Gao, Hu Yin, Jun Wang

“…The new leakage model and numerical method concerning time-step deduction are assessed by solving the issues of fully coupled fracture-wall and fracture-inner systems considering drilling fluid leak-off. …”
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Investigation on Influences of  Two Discrete Methods on Galloping Characteristics of Iced Quad Bundle Conductors by Xiaohui Liu, Guangyun Min, Chuan Wu, Mengqi Cai

“…Finally, based on the numerical method, the displacement response of the two discrete methods is obtained. …”
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Thermodynamics and solar radiative analysis in Jeffery-Hamel flow through non-parallel channel by novel improved residual power series method by Mohamed Bouzidi, Mohsin Ul Haq, Ikram Ullah, Saira Shukat, Hijaz Ahmad, Mohammad Mahtab Alam, Hamid Khan, Marouan Kouki

“…The novel IRPSM, which is sami-numerical method, is utilized to work out on the solutions of obtained system of ODEs. …”
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Electron Acceleration by Multiple Fast Fermi Reflections at Earth’s Bow Shock by Y. Y. Liu, J. B. Cao, C. M. Liu, Y. T. Song, D. K. Hu

“…The spacecraft observation of accelerated electrons is reproduced with a numerical method based on the reflection model. Such an acceleration process may be a potential solution to the injection problem.…”
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Excitation of ULF, ELF, and VLF Resonator and Waveguide Oscillations in the Earth–Atmosphere–Ionosphere System by Lightning Current Sources Connected with Hunga Tonga Volcano Erupt... by Yuriy G. Rapoport, Volodymyr V. Grimalsky, Andrzej Krankowski, Asen Grytsai, Sergei S. Petrishchevskii, Leszek Błaszkiewicz, Chieh-Hung Chen

“…The electromagnetic field is determined from the dynamics in the ionosphere and from a quasi-stationary approach in the atmosphere, considering not only the electric component but also the magnetic one. An analytical/numerical method has been developed to investigate the excitation of the global Schumann resonator and the eigenmodes of the coupled Schumann and ionospheric Alfvén resonators in the ELF range and the eigenmodes of the Earth–ionosphere waveguide in the VLF range. …”
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Study results of the stress-strain states of the crown parts of molars restored with composite, ceramic and zirconium onlays by Y.A. Sardykov, M.H. Kryshchuk, O.O. Fastovets, R.Y. Matvieienko

“…Control was carried out in the form of numerical characteristics and graphical visualization in the EXOCAD program. The numerical method of finite elements, information technologies and program codes of the ANSYS Workbench 12.1 system were used to solve applied problems of biomechanics. …”
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Neuromorphic, physics-informed spiking neural network for molecular dynamics by Vuong Van Pham, Temoor Muther, Amirmasoud Kalantari Dahaghi

“…Compliance with the physical principles, comparable performance to a numerical method, and integration of start-of-the-art ML architectures are top-concerned examples of those gaps. …”
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Curative effect of auricular copper scraping combined with auricular acupoint pressing on insomnia after Methylprednisolone pulse therapy for thyroid-associated ophthalmopathy (耳部铜... by MA Yan (马艳), ZHAO Yue (赵悦), LIN Yuxiao (林育潇), LIU Xiao (刘笑), SONG Yumin (宋玉敏)

“…Objective　Methods 82 patients diagnosed with thyroid-associated ophthalmopathy who needed hormone pulse therapy were randomly divided into control group and observation group according to numerical method, with 41 cases in each group. Patients in both groups were given methylprednisolone pulse therapy. …”
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Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems by Mohammadjavad Mahmoodabadi, Neda Amiri

“…In this way, the performance of the Homotopy Perturbation Method (HPM) is compared with the numerical methods to find the solutions of nonlinear Equations in the vibration field. …”
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Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus by Uğur Kadak, Muharrem Özlük

“…Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. …”
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Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance by Dongmei Zhang, Fangqi Chen

“…With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively. …”
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Numerical Approximation of Fractional-Order Volterra Integrodifferential Equation by Xiaoli Qiang, Kamran, Abid Mahboob, Yu-Ming Chu

“…Therefore, we need numerical methods to invert the solution to the real domain. …”
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Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order by Asma Ali Elbeleze, Adem Kiliçman, Bachok M. Taib

“…This paper presents the application of homotopy perturbation and variational iteration methods as numerical methods for Fredholm integrodifferential equation of fractional order with initial-boundary conditions. …”
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A Review on Soil-Foundation-Interaction Models by Gaurav Pandey, Dhirendra Patel, Vishal Mourya, Rajesh Kumar, Suresh Kumar

“…This parameter can be calculated either through experiments or empirical formulas. Different numerical methods have also been presented along with a few literatures. …”
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Comparative study of parameter extractions of photovoltaic modules using analytical and numerical approaches by Brahim Belmahdi

“…This study seeks to assess and compare various analytical and numerical methods for extracting the primary five parameters of photovoltaic modules. …”
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Physics Informed Neural Networks for Modeling Large-Scale Wind Driven Ocean Circulation by Boohyun An, Mohammad Z. Shanti, Chan Yeob Yeun, Ernesto Damiani, Sungmun Lee, Tae-Yeon Kim

“…This approach highlights the potential of the physics informed neural network to address more complex oceanographic models, where conventional numerical methods may be constrained by data availability and computational cost.…”
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Research of the Pose Forward Solution Algorithm of Stewart Platform based on BP Neural Network by Zhang Zongzhi, Qin Junqi, Chen Hailong, Liu Pingsong

“…Aiming at the problem of low speed of using numerical methods to solve the Stewart platform position and attitude forward solution and the initial value of improper selection may not obtain the forward solution,the BP neural networks algorithm is used for solving those problems.The experiment and simulation results show that this method is fast and effective.…”
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