Dynamic Analysis of Flexible Shaft and Elastic Disk Rotor System Based on the Effect of Alford Force by Wenjun Yang, Huiqun Yuan, Li Hui, Kaifeng Zhang

“…Taken the flexible shaft and elastic disk rotor system as the research object, vibration differential equations are established by the modal synthesis method. …”
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Z2×Z3 Equivariant Bifurcation in Coupled Two Neural Network Rings by Baodong Zheng, Haidong Yin

“…We discuss the spatiotemporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. …”
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Research on Error Propagation Law of Flood Routingby Fourth-order Runge - Kutta Method by ZHOU Bin

“…The fourth-order Runge-Kutta method is one of the commonly used algorithms for solvingordinary differential equations of reservoir flood routing. Studying its error propagation law isof great significance for improving the accuracy of results. …”
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Foundational aspects of a new matrix holomorphic structure by Hedi Khedhiri, Taher Mkademi

“…Originality/value – We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. …”
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Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter by Titilayo Morenike Agbaje, Gilbert Makanda

“…The fluid mathematical model developed from the Navier-Stokes equations resulted in a system of partial differential equations which were then solved by the multidomain bivariate spectral quasilinearization method (MD-BSQLM). …”
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Analytical approach to explore theory of creeping flow with constant absorption by Abdul M. Siddiqui, Q.A. Azim, Getinet A. Gawo, Ayesha Sohail

“…The stream function is used to transform the governing equations to system of ordinary differential equations. The analytical solutions are found for velocity components, pressure distribution, the axial flow rate, the mean pressure drop and the shear stress. …”
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Flap/Lag Stall Flutter Control of Large-Scale Wind Turbine Blade Based on Robust H2 Controller by Tingrui Liu, Wei Xu

“…The aeroelastic partial differential equations are reduced by Galerkin method, with the aerodynamic forces decomposed by strip theory. …”
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Novel Analysis of Fuzzy Fractional Klein-Gordon Model via Semianalytical Method by Mohammad Alshammari, Wael W. Mohammed, Mohammed Yar

“…It is crucial to emphasize that the suggested fuzziness method is intended to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations found in complex and physical structures.…”
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ANTI-VIBRATION OPTIMIZATION DESIGN FOR CLAMP-LIFTING DEVICE ON AIRCRAFT TRACTORS by GAO QingZhen, HUANG An, SHI PeiCheng

“…In order to solve the vibration problem of clamp-lifting device, the joint mechanical analysis and modelings including clamp-lifting device, wheel and landing gear were carried out, and the system vibration differential equations including stiffness and damping characteristics of components were obtained by the frequency response method. …”
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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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Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach by Mrinal Kanti Rajak, Rajen Pudur

“…A comprehensive mathematical model is developed, incorporating the nonlinear dynamics of the PLL system through differential equations and transfer functions. The hybrid optimization framework is formulated as a constrained optimization problem, where PSO provides global search capabilities while GD ensures local convergence. …”
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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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