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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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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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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Experimental Validation of Numerical Model for Bi-Tilt-Isolator by Ming-Hsiang Shih, Wen-Pei Sung, Chia-Yu Ho

“…Then, BTI element of nonlinear analysis program, GENDYN, is developed by the fourth-order Runge-Kutta method, the discretized ordinary differential equation for three movement stages of BTI. Then, test set-up of superstructure installed with BTI is tested and recorded the real displacement and acceleration responses under conditions of full lubrication, mild lubrication, and without lubrication between interface of bi-tilt beveled substrate and slider with three various initial displacements. …”
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Estimating the Force of Infection with Helicobacter pylori in Japan by Taishi Kayano, Ki-Deok Lee, Hiroshi Nishiura

“…Solving the McKendrick partial differential equation model, the seroprevalence was modeled as a function of survey year and age. …”
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Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising by Khursheed Alam, Alka Chauhan, Santosh Kumar

“…The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. …”
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The relative biologic effectiveness versus linear energy transfercurve as an output-input relation for linear cellular systems by Quoc T. Luu, Paul DuChateau

“…Here we introduce a differential equation formulation for a signal-and-system model that sees cells as systems, different radiation types as input, and cellular responses as output. …”
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Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials by Luc Leroy Mambou Ngueyep, Joseph Ndop, Elise Rose Atangana Nkene, Jean-Marie Bienvenu Ndjaka

“…By choosing that the inhomogeneity parameter is between -0.5 and 0.5, we have established the differential equation which describes the equilibrium of the hollow cylinder in rotation under an axial load. …”
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Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak by Tianzeng Li, Yu Wang, Weiqiu Pan

“…To provide the numerical solution of the single-term (or multiterm) fractional-order nonlinear differential equation, the GMMP scheme and Newton method are introduced. …”
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An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells by Patrick W. Nelson, Michael A. Gilchrist, Daniel Coombs, James M. Hyman, Alan S. Perelson

“…We show that this model is a generalization ofthe standard differential equation and of delay models previously used to describeHIV-1 infection, and provides a means for exploring fundamental issuesof viral production and death. …”
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Modeling the Process of Obtaining Liquid Pyrolysis Products of Plant Biomass Taking into Account the Rate of their Cooling by S. V. Vasilevich, M. V. Malko, D. V. Degterov, A. N. Asadchy

“…To assess the effect of the cooling rate of liquid pyrolysis products, a third-order differential equation was used for a model limited by the reaction rate. …”
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Face Boundary Formulation for Harmonic Models: Face Image Resembling by Hung-Tsai Huang, Zi-Cai Li, Yimin Wei, Ching Yee Suen

“…Mapping between the source and target face boundaries with constituent pixels is explored by two approaches: cubic spline interpolation and ordinary differential equation (ODE) using Hermite interpolation. …”
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Numerical modelling of rope elasticity for heave compensation lifting in offshore crane operations by Bassey Asanga, Akanimo Ekpenyong, Aniekan Ikpe

“…The results showed that the developed mathematical model for the wire rope extension (e) derived from second order differential equation found directly proportional to the load applied but inversely proportional to the wire rope stiffness (β)  during WOC and WC were 2.50 × 107 N.m-1 and 3.33 × 107 N.m-1, respectively. …”
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Three-Dimensional Inversion of Borehole-Surface Resistivity Method Based on the Unstructured Finite Element by Zhi Wang, Sinan Fang

“…The forward simulation and calculation start from the partial differential equation and the boundary conditions of the total potential of the three-dimensional point current source field are satisfied. …”
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Application of Image Denoising Method Based on Two-Way Coupling Diffusion Equation in Public Security Forensics by Yiqun Wang, Changpeng He, Zhenjiang Li

“…By improving the second-order partial differential equation, a new diffusion function with better diffusion effect than the original model is constructed. …”
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Integrated movement models for individual tracking and species distribution data by Frances E. Buderman, Ephraim M. Hanks, Viviana Ruiz‐Gutierrez, Michael Shull, Robert K. Murphy, David A. W. Miller

“…We outline a general IMM framework and develop and apply a specific stochastic differential equation model to a case study of telemetry and species distribution data for golden eagles in western North American during spring migration. …”
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Thermal radiation effects of ternary hybrid nanofluid flow in the activation energy: Numerical computational approach by Hakeem Ullah, Syed Arshad Abas, Mehreen Fiza, Aasim Ullah Jan, Ali Akgul, Magda Abd El-Rahman, Seham M. Al-Mekhlafi

“…Methodology: After utilizing von Karman similarity transformations to renovate the principal equations into the set of nonlinear differential equation systems, the resulting equations were solved using the bvp4c numerical approach with the assistance of MATLAB software. …”
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Mathematical Modelling and Analysis of Transmission Dynamics of Lassa Fever by E. A. Bakare, E. B. Are, O. E. Abolarin, S. A. Osanyinlusi, Benitho Ngwu, Obiaderi N. Ubaka

“…In this work, a periodically forced seasonal nonautonomous system of a nonlinear ordinary differential equation is developed that captures the dynamics of Lassa fever transmission and seasonal variation in the birth of Mastomys rodents where time was measured in days to capture seasonality. …”
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Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics by Stefan Schoder

“…PINNs are appealing since they can efficiently integrate a partial differential equation and experimental data by minimizing a loss function. …”
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