Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization by Y. Y. Lee

“…A multistructural/acoustic modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibrations of the flexible panels and acoustic pressure induced within the air gap. …”
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THE DYNAMICS RESEARCH AND TEST VERIFICATION BASED ON THE MISALIGNMENT OF THE HIGH-SPEED SHAFT by HU Yu Nong, ZHANG YueChun, WANG Wen, LI Min, ZHANG Yong

“…According to the force balance and the coordination deformation motion system the establishment of the rotor of the differential equations,obtained exciting force and torque. …”
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T model of growth and its application in systems of tumor-immunedynamics by Mohammad A. Tabatabai, Wayne M. Eby, Karan P. Singh, Sejong Bae

“…We recommend usage of the T growth model forthe growth of tumors as part of any system of differential equations. Use ofthis model within a system will allow more flexibility in representing thenatural rate of tumor growth. …”
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Dynamic Load Performance of a Face Gear Drive in a Spent Fuel Reactor by Guo Mingchao, Zhang Ju, Xu Lei, Kan Chen

“…The dynamic model of the face gear drive is established based on the centralized mass method.The influence of factors such as manufacturing errors and misalignments, time-varying meshing stiffness, corrosion on tooth surfaces, earthquakes on the dynamic performance are taken into consideration to deduce the differential equations of the face gear drive. Runge-Kutta method is applied to solve the differential equation, the dynamic loads under excitations of misalignment, earthquake and corrosion are obtained, and the influence law of these excitations on the dynamic load coefficient is further analyzed. …”
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Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques by Imran Siddique, Khush Bukht Mehdi, M. Ali Akbar, Hamiden Abd El-Wahed Khalifa, Asim Zafar

“…These methods can also be used to extract the novel exact traveling wave solutions for solving any types of integer and fractional differential equations arising in mathematical physics.…”
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Implementing the Vieta–Lucas Collocation Optimization Method for MHD Casson and Williamson Model under the Effects of Heat Generation and Viscous Dissipation by M.M. Khader, A. Eid, M. Adel

“…This method is used to convert the problem’s system of ordinary differential equations (ODEs) into a nonlinear system of algebraic equations. …”
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On Fourier Series of Fuzzy-Valued Functions by Uğur Kadak, Feyzi Başar

“…Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. …”
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Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators by Dumitru Baleanu, J. A. Tenreiro Machado, Carlo Cattani, Mihaela Cristina Baleanu, Xiao-Jun Yang

“…The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.…”
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Oscillator with a Sum of Noninteger-Order Nonlinearities by L. Cveticanin, T. Pogány

“…Mathematical model of the system is a second-order differential equation with a nonlinearity of polynomial type, whose terms are of integer and/or noninteger order. …”
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MAGNETO-ELASTIC PRINCIPAL RESONANCE OF AXIALLY MOVING FERROMAGNETIC PLATE UNDER HARMONIC MAGNETIC FORCE (MT) by CAO TianXiao, HU YuDa

“…For the boundary conditions with two long simply supported edges, the transverse vibration differential equations after variables separation is obtained by Galerkin method. …”
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Numerical simulation of the de-bonding phenomenon of FRCM strengthening systems by Ernesto Grande, Maura Imbimbo, Sonia Marfia, Elio Sacco

“…An analytical solution is determined solving the system of differential equations. In particular, in the first part of the paper a nonlinear shear-stress slip law characterized by a brittle post-peak behavior with a residual shear strength in the post peak phase is introduced for either the lower reinforcement-mortar interface (approach 1) or both the lower and the upper interface (approach 2). …”
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A Vieta–Lucas collocation and non-standard finite difference technique for solving space-time fractional-order Fisher equation by Mohd Kashif

“…By using the properties of Vieta–Lucas polynomials, this technique reduces the nonlinear equations into a system of ordinary differential equations (ODEs). The non-standard finite difference (NSFD) method converts this system of ODEs into algebraic equations which have been solved numerically. …”
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Novel Numerical Scheme for Singularly Perturbed Time Delay Convection-Diffusion Equation by Mesfin Mekuria Woldaregay, Worku Tilahun Aniley, Gemechis File Duressa

“…This paper deals with numerical treatment of singularly perturbed parabolic differential equations having large time delay. The highest order derivative term in the equation is multiplied by a perturbation parameter ε, taking arbitrary value in the interval 0,1. …”
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A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate by Nadia Mohdeb

“…Design/methodology/approach – The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion. …”
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Modeling and Analysis of Unsteady Casson Fluid Flow due to an Exponentially Accelerating Plate with Thermal and Solutal Convective Boundary Conditions by Mehari Fentahun Endalew, Subharthi Sarkar

“…Fundamental equations governing an isotropic incompressible radiative Casson fluid flow are defined through a set of linear partial differential equations, and exact solutions are derived by using the Laplace transform approach. …”
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Analysis of SI models with multiple interacting populations using subpopulations by Evelyn K. Thomas, Katharine F. Gurski, Kathleen A. Hoffman

“…Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. …”
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Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver by R. Mahmood, N. Kousar, M. Yaqub, K. Jabeen

“…All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.…”
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Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes by Xiongwei Liu, Junjun Xu, Xiao Wang, Lizhi Cheng

“…This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number R0 is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. …”
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Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms by Mingzhu Song, Quanxin Zhu, Hongwei Zhou

“…By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. …”
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Differential Quadrature Analysis of Free Vibration of Symmetric Cross-Ply Laminates with Shear Deformation and Rotatory Inertia by Moinuddin Malik, Charles W. Bert

“…By using the trigonometric functions describing the mode shapes between the simply supported edges, the governing plate equations are reduced to ordinary differential equations. The solution of the reduced equations is then sought by the differential quadrature method. …”
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