Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions by Jiaquan Xie, Yongjiang Zheng, Zhongkai Ren, Tao Wang, Guangxian Shen

“…In practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hunting phenomenon of the mechanical system. …”
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Chaotic numerical instabilities arising in the transition from differential to difference nonlinear equations by Alicia Serfaty de Markus

“…For computational purposes, a numerical algorithm maps a differential equation into an often complex difference equation whose structure and stability depends on the scheme used. …”
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A Novel Algorithm for Studying the Effects of Squeezing Flow of a Casson Fluid between Parallel Plates on Magnetic Field by Abdul-Sattar J. A. Al-Saif, Abeer Majeed Jasim

“…The suitable one of similarity transformation conversion laws is proposed to obtain the governing MHD flow nonlinear ordinary differential equation. The resulting equation has been solved by a novel algorithm. …”
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In Situ Bioremediation of Crude Petroleum Oil Polluted Soil Using Mathematical Experimentation by Modupe Elizabeth Ojewumi, Moses Eterigho Emetere, Damilola Elizabeth Babatunde, Joshua Olusegun Okeniyi

“…The parabolic partial differential equation developed was resolved into a system of ordinary differential equations (ODEs) by orthogonal collocation method and the necessary boundary condition was used. …”
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Per‐unit transformation for the combined analysis of multi‐energy integration by Zhang Zhang, Fei Wang, Hui Fan

“…Abstract To handle numerical issues caused by dimensional differences among heterogeneous states in integrated energy systems (IES), this paper proposes a novel per‐unit transformation method and explores its applications to the partial differential equation‐governed models. Initially, a unified IES model is developed, which encompasses both fast and slow dynamics in a generalized form. …”
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Axisymmetric Longitudinal-Bending Waves in a Cylindrical Shell Interacting with a Nonlinear Elastic Medium by Alexander I. Zemlyanukhin, Andrey V. Bochkarev, Lev I. Mogilevich, Ekaterina G. Tindova

“…A nonlinear differential equation is derived which describes the propagation of axisymmetric stationary longitudinal-bending waves in infinite cylindrical shell of Timoshenko type, interacting with the external nonlinear elastic medium. …”
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Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells by A.H. Sofiyev, S.N. Keskin, Ali H. Sofiyev

“…Applying Galerkin method to the latter equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. …”
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Thermal performance of a moving fin with temperature-dependent thermal conductivity in convective and radiative environment by Yanqun Han, Xulong Peng

“…It corresponds to a nonlinear heat transfer problem related to the nonlinear ordinary differential equation (NODE) for the unknown temperature excess. …”
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Mathematical Model of Pipeline Abandonment and Recovery in Deepwater by Xia-Guang Zeng, Meng-Lan Duan, Chen An

“…For this problem a third-order differential equation is used as the governing equation in this paper, rather than the traditional second-order one. …”
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Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics by Rafael A. Penchel, José R. Bergmann, Fernando J. S. Moreira

“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. …”
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Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting by Mustafa Hasanbulli, Svitlana P. Rogovchenko, Yuriy V. Rogovchenko

“…We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. …”
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The Impacts of Reducing the Infection Rate and Infection Source on the Transmission of Emerging Infectious Diseases by Jia-Tong Li

“…The impacts of measures intensity, diagnosis rate, and the start time of taking measures on emerging infectious diseases with infectious capacity during the incubation period are considered comprehensively by using a differential equation model. Results show that for each diagnosis rate, the number of infections and deaths has a phase change structure with respect to the measures intensity. …”
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Stiffness Calculation for Negative Moment Region of Steel-Concrete Composite Beams considering the Influence of Cracking and Interface Slip by Wenlong Cao, Jianqing Bu, Cunbao Zhao, Xueyan Wang, Liping Zhang, Jiren Zhang

“…To evaluate this decrease in the stiffness of SCCBs, a static differential equation is used to derive analytical expressions of interface slip and deflection. …”
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Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams by Menglin Lou, Qiuhua Duan, Genda Chen

“…In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. …”
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Kinetic Analysis for Macrocyclizations Involving Anionic Template at the Transition State by Vicente Martí-Centelles, M. Isabel Burguete, Santiago V. Luis

“…The corresponding differential equation systems for each kinetic model can be solved numerically. …”
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Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams by Tianle Lu, Zhongmin Wang, Dongdong Liu

“…For the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. …”
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A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model by Jian Huang, Zhongdi Cen, Anbo Le

“…By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodifferential equation, which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. …”
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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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