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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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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Method for Calculating Transients in a Gas Pipeline by A. S. Fikov

“…An analytical solution of a system of partial differential equations describing the unsteady isothermal flow of real gases in gas pipelines is considered. …”
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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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Optimized Direct Padé and HPM for Solving Equation of Oxygen Diffusion in a Spherical Cell by M. A. Sandoval-Hernandez, H. Vazquez-Leal, A. Sarmiento-Reyes, U. Filobello-Nino, F. Castro-Gonzalez, A. L. Herrera-May, R. A. Callejas-Molina, R. Ruiz-Gomez

“…This work presents the application of homotopy perturbation method (HPM) and Optimized Direct Padé (ODP) to obtain a handy and easily computable approximate solution of the nonlinear differential equation to model the oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. …”
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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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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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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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Heat and mass transfer performance of power-law nanofluid flow with thermal radiation and joule heating aspects: Surface heat flux analysis by Mhamed Benaissa, Zia Ullah, A. Dahshan, Md Mahbub Alam, Khadijah M. Abualnaja, Hanaa Abu-Zinadah, Abdullah A. Faqihi, Nidhal Ben Khedher

“…The physical problems are converted into a nonlinear ordinary differential equation under the implementation of similarity transformations, stream functions and Keller box method. …”
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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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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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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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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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Existence for Singular Periodic Problems: A Survey of Recent Results by Jifeng Chu, Juntao Sun, Patricia J. Y. Wong

“…We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.…”
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A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach by Taha Aziz, F. M. Mahomed

“…In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. …”
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Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems by P. G. Dlamini, S. S. Motsa, M. Khumalo

“…The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. …”
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SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions by Pengju Duan

“…The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. …”
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