Theory of Frequency Captured of Eccentric Rotor by Vibration Environment with Same Direction by Su Ming, Li Rong, Xie Zhiping, Zheng Jiming

“…An integral mean method with small parameters and periodic coefficient (IMM-SPPC) is proposed, which converts the relative motion of the electrically driven eccentric rotor and the vibration environment into a second-order periodic coefficient differential equation. Through the calculation of the equilibrium point of the second-order periodic coefficient differential equation and the study of its stability, the synchronization criterion and the stability criterion of the eccentric rotor and the vibration environment are deduced. …”
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Bending Vibration Analysis of Tensioned Ball Screw under Nonuniform Stress during the Cutting Process by Cheng Zhang, Jianrun Zhang

“…A method to solve the differential equation under different boundary conditions is proposed based on the segmentation method. …”
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Frequency-Dependent FDTD Algorithm Using Newmark’s Method by Bing Wei, Le Cao, Fei Wang, Qian Yang

“…By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. …”
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Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations by Darae Jeong, Seungsuk Seo, Hyeongseok Hwang, Dongsun Lee, Yongho Choi, Junseok Kim

“…We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. …”
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Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations by Răzvan O. Moşincat, Ciprian Preda, Petre Preda

“…We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C0-semigroup {𝑇(𝑡)}𝑡≥0). …”
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Double Stratified Mixed Convective Flow of Couple Stress Nanofluid past Inclined Stretching Cylinder Using Cattaneo-Christov Heat and Mass Flux Model by Wubshet Ibrahim, Gosa Gadisa

“…The governing partial differential equation of the boundary layer flow region is reduced to its corresponding ordinary differential equation using a similarity transformation technique. …”
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Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation by Irina Perfilieva, Vladik Kreinovich

“…Traditionally, to obtain such large-scale predictions, we first perform a detailed integration of the corresponding differential equation and then average the resulting detailed solution. …”
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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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A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method by Abdelhalim Ebaid, Nwaf Al-Armani

“…Accordingly, the original differential equation is transformed into a singular differential equation with classical boundary conditions. …”
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Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar by Bole Ma, Yongsheng Ren

“…The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. …”
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Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation by Kenneth L. Jones, Xiaogui He, Yunkai Chen

“…An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. …”
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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface by Daud Ahmad, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, Arsha Khalid

“…Instead of solving the partial differential equation, we can find the optimal conditions for which the surface is the extremal of the Dirichlet functional. …”
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Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification by Li-Qun Chen, Hu Ding, C.W. Lim

“…The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. …”
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Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation by F. Waffo Tchuimmo, J. B. Gonpe Tafo, A. Chamgoue, N. C. Tsague Mezamo, F. Kenmogne, L. Nana

“…The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. …”
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Data-driven model discovery and model selection for noisy biological systems. by Xiaojun Wu, MeiLu McDermott, Adam L MacLean

“…Biological systems exhibit complex dynamics that differential equations can often adeptly represent. Ordinary differential equation models are widespread; until recently their construction has required extensive prior knowledge of the system. …”
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The analysis of modyficated mono equation by Donatas Švitra, Renata Retkutė

“… The differential equation with dalay: Ń(t) = α (N(t - h))/(1 +(N(t-h)/K)n) - βN(t),  n > 1 is proposed to model blood cells dynamics. …”
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Approximation of Analytic Functions by Chebyshev Functions by Soon-Mo Jung, Themistocles M. Rassias

“…We solve the inhomogeneous Chebyshev's differential equation and apply this result for approximating analytic functions by the Chebyshev functions.…”
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Logic Structure of Means Used for Higher Dynamic Stability of Power Transmission Systems by G. E. Pospelov

“…The paper contains a proposal for classification of means used for higher dynamic stability of power transmission systems on the basis of a differential equation of generator rotor motion which makes possible to estimate efficiency of these means.…”
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Steady Three-Dimensional MHD Mixed Convection Couple Stress Flow of Hybrid Nanofluid with Hall and Ion Slip Effect by Ali Rehman, Waris Khan, Ebenezer Bonyah, Samsul Ariffin Abdul Karim, Ahmed Alshehri, Ahmed M. Galal

“…To transform the nonlinear partial differential equation to a nonlinear ordinary differential equation we used the defined similarity transformation. …”
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Machine learning to identify environmental drivers of phytoplankton blooms in the Southern Baltic Sea by Maximilian Berthold, Pascal Nieters, Rahel Vortmeyer-Kley

“…We employed generalized additive mixed models to characterize similar blooming patterns and trained an artificial neural network within the Universal Differential Equation framework to learn a differential equation representation of these pattern. …”
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