Optimal control of infectious diseases using vaccination and treatment by Maryam Nikbakht

“…For this purpose, an optimal control problem with the objective function is introduced, and vaccination and treatment are considered control variables.Methodology:  In this study, the necessary control conditions and the existence of optimal control are expressed by applying the control to the SIR-differential equation system. The experimental results are compared with those obtained from the fourth-order runge-kutta scheme. …”
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The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator by Wang Guangbao, Ding Guangtao

“…The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. …”
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Growth-rate distributions of gut microbiota time series by E. Brigatti, S. Azaele

“…Here a neutral model based on a stochastic differential equation with demographic noise, which presents a closed form for these distributions, is used to describe the population dynamics of microbiota. …”
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HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation by Shu-Li Mei, De-Hai Zhu

“…The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. …”
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Analysis and Study on Bending Vibration Frequency of New Corrugated Steel Web Composite Box Girder by Xiaomeng Zang, Genhui Wang, Zichen Zhang

“…In order to accurately analyze the bending vibration frequency of the new composite box girder, the effects of web folding effect, shear lag, and shear deformation are comprehensively considered in this paper, and the elastic control differential equation and natural boundary conditions of the composite box girder are established by using the Hamilton principle. …”
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A weak invariance principle and asymptotic stability for evolution equations with bounded generators by E. N. Chukwu, P. Smoczynski

“…The theory is illustrated with an example of an integro-differential equation of interest in the theory of chemical processes. …”
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Tensile Failure Mechanism of Antiseepage System for Slope with Solid Waste Underground Landfill by Liu Fei, Zhongxi Jiang

“…The analytical solutions of the tensile force and displacement of the antiseepage membrane was calculated through differential equation of equilibrium. With general slag and ardealite slag as the research objects, the major parameters affecting the internal tensile force of the antiseepage membrane were analyzed and studied by the combination of numerical and theoretical methods. …”
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Vibration of a Cylindrical Tunnel under a Centric Point-Source Explosion by Yuetang Zhao, Cheng Chu, Anastasios Vafeidis, Jie Li

“…The governing equation of the motion is a fourth-order partial differential equation, for which a numerical method combining finite difference with the implicit Newmark-β method was adopted. …”
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Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System by Salim Medjber, Hacene Bekkar, Salah Menouar, Jeong Ryeol Choi

“…In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. …”
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Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative by Surendar Kumar Yadav, Mridula Purohit, Murli Manohar Gour, Lokesh Kumar Yadav, Manvendra Narayan Mishra

“…Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. To validate the accuracy of proposed method, we present the analytical solutions of three applications of multi-dimensional fractional diffusion equations. …”
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Complex dynamics of a predator-prey fishery model: The impact of the Allee effect and bilateral intervention by Yuan Tian, Yang Liu, Kaibiao Sun

“…The existence and stability of the order-1 periodic solution and the order-2 periodic solution of the control system are analyzed by using the differential equation geometry theory. Additionally, numerical simulations are carried out to verify the correctness of the conclusions, and illustrate the impact of the Allee effect and bilateral intervention on the ecosystem, which provides an effective method for modern fishery conservation and harvesting.…”
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A Spatial Euler-Bernoulli Beam Element for Rigid-Flexible Coupling Dynamic Analysis of Flexible Structures by Zhigang Zhang, Zhaohui Qi, Zhigang Wu, Huiqing Fang

“…Thus all the high frequencies can be filtered out and a corresponding equivalent internal damping will be produced in this new formulation, which can improve the computation performance of the proposed element for solving the stiff problem and evaluate the governing equations even by using the nonstiff ordinary differential equation solver. Finally, several numerical examples are carried out to verify the validation and efficiency of this proposed formulation by comparison with the analytical solutions and other research works.…”
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A Finite Difference Method for Solving Unsteady Fractional Oldroyd-B Viscoelastic Flow Based on Caputo Derivative by Fang Wang, Yu Wang

“…In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by integrating by parts instead of by direct discretization. …”
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Richards equation for the assessment of landslide hazards by Ramesh Chandra Timsina

“…However, as a highly nonlinear parabolic partial differential equation (PDE), it has limited analytic solutions, which often lack precision in practical scenarios. …”
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Comparative Studies of Nonlinear Models and Their Applications to Magmatic Evolution and Crustal Growth of the Huai’an Terrane in the North China Craton by Qiuming Cheng, Min Gao

“…This paper introduces these nonlinear functions derived from a unified differential equation, with parameters that reflect their relative nonlinearities and singularities, enabling their comparative application. …”
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Analysis of Bianchi Type V Holographic Dark Energy Models in General Relativity and Lyra’s Geometry by Daba Meshesha Gusu, M. Vijaya Santhi

“…The solutions of differential equation fields have been obtained by considering two specific cases, namely, the expansion scalar θ in the model is proportional to the shear scalar σ and the average scale factor taken as hybrid expansion form. …”
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Numerical Solutions of Duffing Van der Pol Equations on the Basis of Hybrid Functions by M. Mohammadi, A. R. Vahidi, T. Damercheli, S. Khezerloo

“…The next technique is to convert this equation into a system of ordinary differential equation of the first order (SODE) and solve it according to the proposed approximate method. …”
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Trivariate Stochastic Weather Model for Predicting Maize Yield by Patrick Chidzalo, Phillip O. Ngare, Joseph K. Mung’atu

“…Stochastic analyses are applied on the pdf and process to account for nonlinearity and nonstationarity, and also establish a corresponding stochastic differential equation (SDE) for maize yield. The trivariate stochastic process predicts maize yield with R2=0.8389 and MAPE=4.31% under a deep learning framework. …”
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Numerical Simulation of Dynamic Response of Submerged Floating Tunnel under Regular Wave Conditions by Wenlong Luo, Bo Huang, Yao Tang, Hao Ding, Ke Li, Liang Cheng, Qingyang Ren

“…In this model, wave-induced hydrodynamic loads are estimated by the Morison equation for a moving object, and the simplified governing differential equation of the tunnel with mooring cables is solved using the fourth-order Runge–Kutta and Adams numerical method. …”
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Nonlinear compressive reduced basis approximation for PDE’s by Cohen, Albert, Farhat, Charbel, Maday, Yvon, Somacal, Agustin

“…Linear model reduction techniques design offline low-dimensional subspaces that are tailored to the approximation of solutions to a parameterized partial differential equation, for the purpose of fast online numerical simulations. …”
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