A Novel Procedure in Scrutinizing a Cantilever Beam with Tip Mass: Analytic and Bifurcation by Asma Alanazy, Galal M. Moatimid, T. S. Amer, Mona A. A. Mohamed, M. K. Abohamer

“…He’s frequency formula (HFF) is utilized with the non-perturbative approach (NPA) to transform the nonlinear governing ordinary differential equation (ODE) into a linear form. Mathematica Software 12.0.0.0 (MS) is employed to confirm the high accuracy between the nonlinear and the linear ODE. …”
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Development of a computational model of glucose toxicity in the progression of diabetes mellitus by Danilo T. Pérez-Rivera, Verónica L. Torres-Torres, Abraham E. Torres-Colón, Mayteé Cruz-Aponte

“…One large stride that is being made is the generation of techniques to assist physicians to ``personalize medicine''.From available physiological data, biological understanding of the system, and dimensional analysis, a differential equation-based mathematical model was built in a sequential matter, to be able to elucidate clearly how each parameter correlates to the patient's current physiological state. …”
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A Novel Version of HPM Coupled with the PSEM Method for Solving the Blasius Problem by Uriel Filobello-Nino, Hector Vazquez-Leal, Jesus Huerta-Chua, Victor Manuel Jimenez-Fernandez, Mario Alberto Sandoval-Hernandez, Enrique Delgado-Alvarado, Victor Manuel Tlapa-Carrera

“…This work studies the nonlinear differential equation that models the Blasius problem (BP) which is of great importance in fluid dynamics. …”
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Linearized Harmonic Balance Method for Seeking the Periodic Vibrations of Second- and Third-Order Nonlinear Oscillators by Chein-Shan Liu, Chung-Lun Kuo, Chih-Wen Chang

“…The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. …”
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Traffic Anomaly Detection Algorithm for Wireless Sensor Networks Based on Improved Exploitation of the GM(1,1) Model by Qin Yu, Jibin Lyu, Lirui Jiang, Longjiang Li

“…Based on our systematical researches on the characteristics of WSN traffic, the causes of WSN abnormal traffic, and latest related research and development, we better exploit the GM(1,1) model following four guidelines: using a sliding window to determine historical data for modeling, optimizing initial value of one-order grey differential equation, making traffic prediction by short step exponential weighted average method, and judging whether the traffic of the next moment is abnormal by Euclidean distance. …”
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Using the Nonuniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations by Brenton T. Hall, Ching-Shan Chou, Jen-Ping Chen

“…Partial Differential Equation simulations can produce large amounts of data. …”
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Partial Volume Reduction by Interpolation with Reverse Diffusion by Olivier Salvado, Claudia M. Hillenbrand, David L. Wilson

“…The gray level of each subvoxel is considered as “material” able to move between subvoxels but not between voxels. A partial differential equation is written to allow the material to flow towards the highest gradient direction, creating a “reverse” diffusion process. …”
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STABILITY ANALYSIS OF SPHERICAL HYBRID SLIDING BEARINGS CONSIDERING BOUNDARY SLIP STATE by CHENG Pan, SHEN JingFeng, QIN Wei, XUE Hao, ZHU Rui

“…For the transient Reynolds equation in the boundary slipstate, the equation uses the small perturbation method to derive the partial differential equation of the perturbation pressure, and combines the finite difference method and the relaxation iterative method to solve the equation to obtain the stiffness and damping coefficient of the ball bearing under the state of boundary slip, and then establish the shafting trajectory equation to solve the instability speed. …”
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Numerical Simulation of Thermo-Hydro-Mechanical Coupling of Model Test for Nuclear Waste Disposal by Yu-Ping Wang, Zhe Wang, Fa-Cheng Yi, Lei Fu, Ying Luo

“…Using the buffer material Mock-up test of multi-field coupling as a model, the partial differential equation (PDE) module in the general finite element software COMSOL Multiphysics was developed by a second development stage. …”
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A deep-learning approach to parameter fitting for a lithium metal battery cycling model, validated with experimental cell cycling time series by Maria Grazia Quarta, Ivonne Sgura, Elisa Emanuele, Jacopo Strada, Raquel Barreira, Benedetto Bozzini

“…This study contributes to shedding light on this highly technologically relevant problem, thanks to the combination of quantitative data exploitation and Partial Differential Equation (PDE) modelling for metal anode cycling. …”
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High-resolution analysis of hydraulic response characteristics of silted stormwater pipeline and manholes in urban catchments using GASM-TranGRU and CFD-DEM by Danyang Di, Ruoyi Wang, Hongyuan Fang, Mingsheng Shi, Bin Sun, Niannian Wang, Bin Li

“…The vibrational differential equation of the ‘silted pipeline-manhole' system is then adopted to quantify the physical boundary constraints on the fluid–solid coupling relationship. …”
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Graded transcendental functions: an application to four-point amplitudes with one off-shell leg by Thomas Gehrmann, Johannes Henn, Petr Jakubčík, Jungwon Lim, Cesare Carlo Mella, Nikolaos Syrrakos, Lorenzo Tancredi, William J. Torres Bobadilla

“…We describe the derivation of canonical differential equation systems and present a method for fixing boundary conditions without the need for a full functional representation. …”
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A Hybrid Renewable Sources Implementation for a DC Microgrid with Flatness-Nonlinear Control to Achieve Efficient Energy Management Strategy by Furqan A. Abbas, Adel A.Obed, Ammar Alhasiri, Salam J. Yaqoob

“…Because of the nonlinear system's behavior, differential flatness-based control has been applied mainly in nonlinear systems where the number of variables to the outputs is reduced with a robust control system established through inherited parameter reductions and equality constraints due to the system trajectories (x, u) is straightforwardly estimated from flat output trajectories y and their derivatives without any differential equation integration. The PI control is executed when the SC adjusts the DC bus voltage variation. …”
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A Coupled Thermo-Hydromechanical Model of Soil Slope in Seasonally Frozen Regions under Freeze-Thaw Action by Yongxiang Zhan, Zheng Lu, Hailin Yao, Shaohua Xian

“…Based on the partial differential equation defined using the COMSOL Multiphysics software, a thermo-hydromechanical coupling model considering water migration, ice-water phase change, ice impedance, and frost heave is constructed, and the variations in the temperature field, migration of liquid water, accumulation of solid ice, and deformation of frost heave in frozen soil slopes are analysed. …”
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Pressure-Predicting Model for Ultralow-Permeability Reservoirs considering the Water Absorption Characteristics of Mudstone Formations by Kai Liu, Daiyin Yin, Yong Wang

“…Combining the material balance method and finite difference method, the space terms in the basic differential equation are replaced by the material balance equation, and the finite difference in the time term is obtained. …”
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Organizational and technological principles of building condition monitoring at the stage of life cycle operation by S. V. Fedosov, A. A. Lapidus, A. B. Petrukhin, B. E. Narmaniya

“…The mathematical operator of the Cauchy problem, which consists in finding a solution to an ordinary differential equation of the first order, can be used to establish the state of a concrete structure at any period of the life cycle.Results. …”
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Modeling of Electric Field and Dielectrophoretic Force in a Parallel-Plate Cell Separation Device with an Electrode Lid and Analytical Formulation Using Fourier Series by Daiki Nishikawa, Yoshinori Seki, Shigeru Tada

“…The solution was approximated by extrapolating a novel approximate equation as a boundary condition for the potential between adjacent fingers of interdigitated electrodes and changing the underlying differential equation into a solvable form. The distributions of the potential and electric fields obtained by the analytical solution were compared with those from numerical simulations using finite element method software to verify their accuracy. …”
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Partial Volume Reduction by Interpolation with Reverse Diffusion

“…The gray level of each subvoxel is considered as “material” able to move between subvoxels but not between voxels. A partial differential equation is written to allow the material to flow towards the highest gradient direction, creating a “reverse” diffusion process. …”
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Advanced technique for flexible cable analysis by A. V. Chesnokov, V. V. Mikhailov

“…The technique proposed is based on the sine-series expansion of the external load and the shape function of the flexible cable. The differential equation of cable equilibrium is thus transformed into the set of algebraic equations. …”
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THE SOLUTION TO THE PROBLEM OF USING GROUND WATER TO COOL LIVESTOCK BUILDINGS by Thay Ngok Shon, Vo Ti Tin

“…For this purpose, the authors have created a heat balance equation at steady state for any infinitesimal element of the fin, and solved the differential equation afterwards. The authors applied the results for calculating practical problem of ground water irrigation of a roof of a livestock shed made of metal areas tiles.…”
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