Thermal Diffusivity Identification of Distributed Parameter Systems to Sea Ice by Liqiong Shi, Zhijun Li, Enmin Feng, Yila Bai, Yu Yang

“…A method of optimal control is presented as a numerical tool for solving the sea ice heat transfer problem governed by a parabolic partial differential equation. Taken the deviation between the calculated ice temperature and the measurements as the performance criterion, an optimal control model of distributed parameter systems with specific constraints of thermal properties of sea ice was proposed to determine the thermal diffusivity of sea ice. …”
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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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High-Accurate Numerical Schemes for Black–Scholes Models with Sensitivity Analysis by Samir Kumar Bhowmik, Jakobin Alam Khan

“…The significance of both the linear and nonlinear Black-Scholes partial differential equation model is huge in the field of financial analysis. …”
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Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes by A. R. Appadu

“…Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. …”
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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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New Numerical Solution of von Karman Equation of Lengthwise Rolling by Rudolf Pernis, Tibor Kvackaj

“…The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. …”
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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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Study on dynamics characteristic on combination misalignment and rubbing of the dual-rotor system by YAO Xia, NAN Guofang, LI Yao, QIU Xuewen

“…The misalignment of the dual-rotor system for the aero-engine will lead to abnormal increase of the vibration which results in the rotor-stator rubbing and affects the safty and stability of the rotor operation.The dual-rotor system was taken as the research object.Considering the combination misalignment-rubbing fault, the dynamic model of the rotor system is established based on the lumped mass method.The differential equation of the system motion was established according to the Lagrange equation, and the Range-Kutta method was used to solve it.The influence mechanism of the key parameters such as the speed, the misalignment angle and the coupling misalignment on the nonlinear dynamic characteristics of the system was studied.The results show that the system presents complex dynamic characteristics such as periodic, multi-periodic, quasi-periodic and chaotic motion with the increase of the rotor’s speed.When the speed is in the range of 1 500-2 200 rad/s, the system switches between periodic 2 motion and chaotic state through multiple paroxysmal bifurcations and paroxysmal inverted bifurcations.There are nonlinear phenomena such as jump in the bifurcation diagram of the vibration response with the change of the parallel misalignment of the coupling.As the misalignment angle of the bearing increases, the chaotic interval of the high speed decreases, and the stable periodic motion interval increases.…”
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A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method by Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, Mohammad W. Alomari

“…This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. …”
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