Experimental Validation of Elliptical Fin-Opening Behavior by James M. Garner, Paul Weinacht, Robert P. Kaste

“…A second order differential equation was used to model elliptical fin deployment history and accounts for: deployment with respect to the geometric properties of the fin, the variation in fin aerodynamics during deployment, the initial yaw effect on fin opening, and the variation in deployment speed based on changes in projectile spin. …”
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Magnetoelastic Principal Parametric Resonance of a Rotating Electroconductive Circular Plate by Zhe Li, Yu-da Hu, Jing Li

“…The axisymmetric parameter vibration differential equation of the variable-velocity rotating circular plate is obtained through the application of Galerkin integral method. …”
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Analytical Method for Capped Pile–Soil Interaction considering the Load Action of Soil under the Pile Cap by Shilin Luo, Mingquan Liu, Jianqing Jiang, Ailifeila Aierken, Jin Chang, Xuewen Zhang, Rui Zhang

“…The theoretical expressions of axial force and load-settlement curves are also achieved by means of establishing and solving the equilibrium differential equation of the pile body. Comparison of calculation results with the ordinary pile indicates that soil load under the pile cap reduces the lateral friction value; the influenced depth is about four times of the load action radius. …”
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Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model by Congyin Fan, Kaili Xiang, Peimin Chen

“…Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. …”
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An innovative analytical method utilizing aboodh residual power series for solving the time-fractional newell-whitehead-segel equation by Seyed Edalatpanah, Eisa Abdolmaleki

“…One of the key advantages of our approach is that the Aboodh transformation operator converts the fractional differential equation into an algebraic equation, thereby significantly reducing the computational effort required in the subsequent algebraic steps. …”
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A stochastic model for water-vegetation systems and the effect of decreasing precipitation on semi-arid environments by Shannon Dixon, Nancy Huntly, Priscilla E. Greenwood, Luis F. Gordillo

“…The model, a stochastic differential equation approximation derived from a Markov jump process, is used to generate extensive simulations that suggest a relationship between precipitation reduction and the desertification process, which might take several years in some instances.…”
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Aggregation and environmental transmission in chronic wasting disease by Olga Vasilyeva, Tamer Oraby, Frithjof Lutscher

“…Wedevelop a strategic differential equation model for ChronicWasting Disease and include direct and indirect transmission aswell as host aggregation into our model. …”
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Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem by Min Jia, Xin Liu, Xuemai Gu

“…The existence, uniqueness, and asymptotic behavior of positive solutions to the singular nonlocal integral boundary value problem for fractional differential equation are obtained. Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method.…”
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Global dynamics of a vector-host epidemic model with age of infection by Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva

“…In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. …”
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Flow between caoxial rotating disks: with and without externally applied magnetic field by R. K. Bhatnagar

“…The governing system of a pair of non-linear ordinary differential equation is solved by treating Reynolds number to small. …”
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Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases by Sara Y. Del Valle, J. M. Hyman, Nakul Chitnis

“…The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease.We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. …”
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Optimal investment game for two regulated players with regime switching by Lin Xu, Linlin Wang, Hao Wang, Liming Zhang

“…In the first case, the associated Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation was an elliptic partial differential equation (PDE). By solving an auxiliary problem, we demonstrated the existence and regularity of the value function. …”
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Variational analysis for simulating free-surface flows in a porous medium by Shabbir Ahmed, Charles Collins

“…A variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. …”
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Preface by Azmy S. Ackleh, Linda J. S. Allen, Graciela Canziani, Shandelle M. Henson, Jia Li, Zhien Ma

“…In Athens, he became interested inecotoxicology and partial differential equation models ofphysiologically structured populations. …”
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Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment by Bing Liu, Shi Luan, Yinghui Gao

“…In this paper, based on impulsive differential equation, the dynamics of a single-species model with impulsive pollution treatment at fixed time in a polluted environment is considered, in which we assume that the species is directly affected by the pollutants. …”
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Laminar Motion of the Incompressible Fluids in Self-Acting Thrust Bearings with Spiral Grooves by Cornel Velescu, Nicolae Calin Popa

“…Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the “pumping” direction. …”
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Experimental Investigation and Analysis of Dynamic Buckling of Drill String in Horizontal Well by Fushen Ren, Baojin Wang, Lei Zhao, Anhe Zhu

“…This paper focuses on the rotational drill string in horizontal well. The differential equation of the dynamic buckling is established considering some various factors, including friction, the drill string-borehole interaction, and rotation, and the equations of the critical load of the sinusoidal buckling and the spiral buckling are derived. …”
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A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet by Sachin Kumar, Jinde Cao, Xiaodi Li

“…In this research work, we focused on finding the numerical solution of time-fractional reaction-diffusion and another class of integro-differential equation known as the integro reaction-diffusion equation. …”
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POSFUST RELIABILITY OF A NON-REPAIRABLE MULTI-STATE SYSTEM WITH POSFUST FAILURE RATE ESTIMATION by Harendra Yadav, Mukesh Kumar Sharma, Vishnu Narayan Mishra

“…In this approach, Markov process (multi-state system) is used for getting the governing differential equation for transition from one state to another state. …”
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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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