A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem by Marcelo Franco de Oliveira, Daniele Cristina Thoaldo, Rodrigo Dias

“…In this approach, a weighting function with respect to time is used in the fundamental differential equation. By assuming a linear variation in some time interval, a time integration is performed. …”
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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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Study on Galloping Oscillation of Iced Catenary System under Cross Winds by Guo Chen, Yiren Yang, Yang Yang, Peng Li

“…The partial differential vibration equation of the system is converted into the ordinary differential equation by the Galerkin method and then numerically solved. …”
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Parameter Identification and Adaptive Control of Uncertain Goodwin Oscillator Networks with Disturbances by Jianbao Zhang, Wenyin Zhang, Chengdong Yang, Haifeng Wang, Jianlong Qiu, Fawaz Alsaadi

“…This paper investigates the dynamic properties of a differential equation model of mammals’ circadian rhythms, including parameter identification, adaptive control, and outer synchronization. …”
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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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Three-Party Stochastic Evolutionary Game Analysis of Reward and Punishment Mechanism for Green Credit by Qingfeng Zhu, Kaimin Zheng, Yilin Wei

“…We gave sufficient conditions for the stability of strategy based on the stability discriminant theorem of Ito^'s stochastic differential equation (SDE). Then, we discussed the impacts of incentive and penalty parameters on green credit. …”
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A note on the global properties of an age-structured viral dynamic model with multiple target cell populations by Shaoli Wang, Jianhong Wu, Libin Rong

“…We also show that under some scenarios the age-structured model can be reduced to an ordinary differential equation system with or without time delays.…”
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Optimal Treatment Strategies for HIV with Antibody Response by Yinggao Zhou, Kuan Yang, Kai Zhou, Chunling Wang

“…An HIV model of ordinary differential equation, which includes immune response, neutralizing antibodies, and multidrug effects, is improved. …”
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The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator by Jevgeņijs Carkovs, Jolanta Goldšteine, Kārlis Šadurskis

“…If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the average motion. …”
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Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator by Sudhansu Palei, Madan Mohan Soren, Daniel Breaz, Luminiţa-Ioana Cotîrlǎ

“…Furthermore, we employ the existence of univalent solutions to a <i>q</i>-differential equation connected with a fractional <i>q</i>-integral operator of fractional order. …”
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Dynamics Analysis of a Class of Delayed Economic Model by Chuangxia Huang, Changlin Peng, Xiaohong Chen, Fenghua Wen

“…This investigation aims at developing a methodology to establish stability and bifurcation dynamics generated by a class of delayed economic model, whose state variable is described by the scalar delay differential equation of the form d2p(t)/dt2=−μδ(p(t))(dp(t)/dt)−μbp(t−τ1) −μ(a0p(t−τ2)/(a1+p(t−τ2)))+μ(d0−g0). …”
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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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An Improved C-V Model and Application to the Coal Rock Mesocrack Images by Yulong Chen, Hongwei Zhang

“…In order to accurately and comprehensively obtain information about coal rock mesocrack images, image processing technique based on partial differential equation (PDE) is introduced in order to expound on the active contour model without edges and overcome the deficiency of the C-V model. …”
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Time Series Prediction Based on Complex-Valued S-System Model by Bin Yang, Wenzheng Bao, Yuehui Chen

“…The experiment results show that the predicted data are very close to the target ones and our method could obtain the better RMSE, MAP, MAPE, POCID, R2, and ARV performances than ARIMA, radial basis function neural network (RBFNN), flexible neural tree (FNT), ordinary differential equation (ODE), and S-system.…”
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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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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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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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Numerical Solutions of Micropolar Nanofluid over an Inclined Surface Using Keller Box Analysis by Khuram Rafique, Hammad Alotaibi, Taher A. Nofal, Muhammad Imran Anwar, Masnita Misiran, Ilyas Khan

“…Compatible transformations are implemented to attain the nonlinear differential equation from the boundary value PDE’s. The physical quantities of practical interest are treated by graphically as well as numerically. …”
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Simulation and Domain Identification of Sea Ice Thermodynamic System by Bing Tan, Peng Lu, Zhijun Li, Enmin Feng, Juan Wang

“…Based on the measured data and characteristics of sea ice temperature distribution in space and time, this study is intended to consider a parabolic partial differential equation of the thermodynamic field of sea ice (coupled by snow, ice, and sea water layers) with a time-dependent domain and its parameter identification problem. …”
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