Application of Adaptive Image Restoration Algorithm Based on Sparsity of Block Structure in Environmental Art Design by Bo Liang, Xin-xin Jia, Yuan Lu

“…This paper proposes a color image restoration method that adaptively determines the size of dictionary atoms and discusses a model based on the partial differential equation restoration method. Through simulation experiments combined with subjective and objective standards, the repair results are evaluated and analyzed. …”
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μ Robust Stable Extrapolation of a Stationary Random Process with Interval Limited Variance by Igor G. Sidorov

“…This approach, unlike others (for example, probabilistic), always ensures the existence of a stable result and solution of a single optimum in the problem of interval minimax extrapolation due to regularization by a small parameter with a derivative of the eigenfunction of a singularly perturbed integro-differential equation of the first order with an integral operator of the Voltaire type of the second kind, defined by a symmetric, closed real the core. …”
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Effect of Tooth Surface Friction on Bending Torsional Axial Pendular Coupling Nonlinear Amplitude Frequency Characteristic of Marine Herringbone Gear by Haoqin Zhang, Hao Dong, Libang Wang, Xiaolong Zhao

“…The Runge-Kutta numerical method is used to solve the differential equation. The phase diagram and time history diagram of the non-dimensional frequency system under the influence of tooth surface friction are obtained. …”
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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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Numerical Simulation of Dynamic Response of Submerged Floating Tunnel under Regular Wave Conditions by Wenlong Luo, Bo Huang, Yao Tang, Hao Ding, Ke Li, Liang Cheng, Qingyang Ren

“…In this model, wave-induced hydrodynamic loads are estimated by the Morison equation for a moving object, and the simplified governing differential equation of the tunnel with mooring cables is solved using the fourth-order Runge–Kutta and Adams numerical method. …”
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Tracking Control of Wave-Adaptive Modular Unmanned Surface Vehicle Using Time-Delay Zeroing Neural Network by Pengfei Guo, Wenyue Zhang, Zheng Li, Zheng Zheng

“…The consistency of the proposed tracking controller is established through ordinary differential equation theory. We conduct a series of simulations, and the results demonstrate the effectiveness and advantages of our higher-order tracking controller based on the multiple ZNN model with time delay in managing the tracking control challenges of the WAMV-VMD system.…”
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Determining the First Probability Density Function of Linear Random Initial Value Problems by the Random Variable Transformation (RVT) Technique: A Comprehensive Study by M.-C. Casabán, J.-C. Cortés, J.-V. Romero, M.-D. Roselló

“…Deterministic differential equations are useful tools for mathematical modelling. …”
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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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Reducing M2 macrophage in lung fibrosis by controlling anti-M1 agent by Fatemeh Bahram Yazdroudi, Alaeddin Malek

“…The study employs a two-step process of discretization followed by optimization, utilizing the Galerkin spectral method to transform the M2 diffusion PDE into an algebraic system of ordinary differential equations (ODEs). The optimal control problem is then solved using Pontryagin/s minimum principle, canonical Hamiltonian equations, and extended Riccati differential equations. …”
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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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Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative by Surendar Kumar Yadav, Mridula Purohit, Murli Manohar Gour, Lokesh Kumar Yadav, Manvendra Narayan Mishra

“…Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. To validate the accuracy of proposed method, we present the analytical solutions of three applications of multi-dimensional fractional diffusion equations. …”
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Entropy framework of the bioconvective Williamson nanofluid flow over a Riga plate with radiation, triple stratification and swimming microorganisms by K. Loganathan, N. Thamaraikannan, S. Eswaramoorthi, Reema Jain

“…Utilizing a suitable conversion approach, translate the partial differential equation (PDEs) system into ordinary differential equations (ODEs). …”
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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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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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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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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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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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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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