An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges by Xue Kai, Wang Jiufa, Li Qiuhong, Wang Weiyuan, Wang Ping

“…The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. …”
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Backward Anticipated Social Optima: Input Constraints and Partial Information by Shujun Wang

“…Furthermore, differently from the classic social optima literature, the dynamics in this framework are driven by <i>anticipated</i> backward stochastic differential equations (ABSDE) in which the <i>terminal</i> instead of the <i>initial</i> condition is specified and the anticipated terms are involved. …”
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Nonlinear Vibration Analysis of Submerged Floating Tunnel Tether by Sheng-nan Sun, Zhi-bin Su, Yun-fen Feng

“…According to the linear vibration mode of tether, the partial differential equation is converted into ordinary differential equations by Galerkin method and the nonlinear vibration equation of tether for the in-plane first four modes and the out-of-plane first four modes are obtained. …”
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Parallel Simulation of HGMS of Weakly Magnetic Nanoparticles in Irrotational Flow of Inviscid Fluid by Kanok Hournkumnuard, Banpot Dolwithayakul, Chantana Chantrapornchai

“…The two-dimensional problem of particle transport under the influences of magnetic force and fluid flow is considered in an annular domain surrounding the wire with inner radius equal to that of the wire and outer radius equal to various multiples of wire radius. The differential equations governing particle transport are solved numerically as an initial and boundary values problem by using the finite-difference method. …”
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Simulating Smoke Filling in Big Halls by Computational Fluid Dynamics by W. K. Chow, C. L. Chow, S. S. Li

“…Mathematical aspects concerning of discretization of partial differential equations and algorithms for solving the velocity-pressure linked equations are briefly outlined. …”
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An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs by Eman S. Alaidarous, Malik Zaka Ullah, Fayyaz Ahmad, A.S. Al-Fhaid

“…The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. …”
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PDE Modeling of a Microfluidic Thermal Process for Genetic Analysis Application by Reza Banaei Khosroushahi, Horacio J. Marquez, Jose Martinez-Quijada, Christopher J. Backhouse

“…The general partial differential equations describing the dynamics of the system are separated into steady-state and transient parts which are derived for a carefully chosen three-dimensional axisymmetric model. …”
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MHD Heat and Mass Transfer of Chemical Reaction Fluid Flow over a Moving Vertical Plate in Presence of Heat Source with Convective Surface Boundary Condition by B. R. Rout, S. K. Parida, S. Panda

“…The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. …”
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A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations by S. S. Motsa, V. M. Magagula, P. Sibanda

“…This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. …”
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Fluid-Induced Vibration Elimination of a Rotor/Seal System with the Dynamic Vibration Absorber by Qi Xu, Junkai Niu, Hongliang Yao, Lichao Zhao, Bangchun Wen

“…The numerical method is used for the solutions of the nonlinear differential equations. The nonlinear responses of the rotor/seal system without and with the absorber are obtained, and then the rotating speed ranges by which the fluid-induced instability can be eliminated completely and partially are presented, respectively. …”
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Unstructured Grids and the Multigroup Neutron Diffusion Equation by German Theler

“…It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. …”
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Nonrigid Registration of Monomodal MRI Using Linear Viscoelastic Model by Jian Yang, Yang Chen, Jingfan Fan, Songyuan Tang

“…After global registration, the local shape variations are assumed to have the properties of the Maxwell model of linear viscoelasticity, and the deformation fields are constrained by the corresponding partial differential equations. To speed up the registration, an adaptive force is introduced according to the maximum displacement of each iteration. …”
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Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations by Meilan Qiu, Liquan Mei, Dewang Li

“…The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations.…”
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Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…Physically existent things utilize partial differential equations as a method of derivation. By using dimensionless variables, the underlying PDEs are dimensionless. …”
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Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment by Brandy Rapatski, Juan Tolosa

“…We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'' scenario model includingtesting and treatment in the SFCCC epidemic.We use compartmental, population-level models,described by systems ofordinary differential equations.We find the basic reproductive number $R_0$ for each system,and we prove that if $R_0<1 the="" system="" has="" only="" the="" disease-free="" equilibrium="" dfe="" which="" is="" locally="" and="" globally="" stable="" whereas="" if="" r_0="">1$, the DFE is unstable.In addition, when $R_0>1$, both systems have a unique endemic equilibrium (EE).We show that treatment alone would not have stopped the San Francisco MSM epidemic,but would have significantly reduced its impact.…”
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MAC Layer Energy Consumption and Routing Protocol Optimization Algorithm for Mobile Ad Hoc Networks by Yaohua Chen, Waixi Liu

“…In order to solve the problem that the analytic solution of differential equations cannot be obtained in the model, a numerical solution of the optimization algorithm is proposed based on the implicit Runge–Kutta method. …”
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Starlikeness associated with certain strongly functions by Afis Saliu, Kanwal Jabeen, Jianhua Gong, Sarfraz Nawaz Malik, Hala Alaqad

“…It also finds the solutions to first-order differential equations and utilizes these results together with the differential subordination developed by Miller and Mocanu to obtain the conditions so that some first-order differential relations associated with ϕλ are subordinate to certain Ma and Minda functions. …”
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Implementing the Galerkin Method Associated with the Shifted Vieta-Lucas Polynomials for Studying Numerically the Bionanofluid Flow Which Is Saturated by Gyrotactic Microorganisms... by M. M. Khader, M. M. Babatin, Ahmed M. Megahed, A. Eid

“…The shifted Vieta-Lucas polynomials are then used as basis functions on the provided domain to solve the nonlinear system of ordinary differential equations that has been constructed (ODEs). The results are presented in the form of graphs and tables to assess the impact of the problem’s governing parameters. …”
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Analyzing Axial Stress and Deformation of Tubular for Steam Injection Process in Deviated Wells Based on the Varied (T,P) Fields by Yunqiang Liu, Jiuping Xu, Shize Wang, Bin Qi

“…The varied temperature and pressure fields were researched by the coupled differential equations concerning mass, momentum, and energy equations instead of traditional methods. …”
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A Theoretical Model of Listeriosis Driven by Cross Contamination of Ready-to-Eat Food Products by C. W. Chukwu, F. Nyabadza

“…In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. …”
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