Guidance Law and Neural Control for Hypersonic Missile to Track Targets by Wenxing Fu, Binbin Yan, Xiaofei Chang, Jie Yan

“…Because the flight dynamics of a hypersonic vehicle is nonlinear, uncertain, and highly coupled, the controller design is challenging, especially to design its guidance and control law during the attack of a maneuvering target. …”
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Designing the Adaptive Tracking Controller for Uncertain Fully Actuated Dynamical Systems with Additive Disturbances Based on Sliding Mode by Chi Nguyen Van

“…This control method is applied to the angles tracking control of the twin rotor multi-input multi-output system (TRMS) which have nonlinear characteristics, the input torque disturbances and the coupling between the horizontal and vertical movements. …”
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Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions by Jiqiang Jiang, Lishan Liu, Yonghong Wu

“…By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: −u′′(t)=λ[f(t,u(t))−q(t)], 0<t<1, αu(0)−βu′(0)=∫01u(s)dξ(s), γu(1)+δu′(1)=∫01u(s)dη(s), where λ>0 is a parameter; f:(0,1)×(0,∞)→[0,∞) is continuous; f(t,x) may be singular at t=0, t=1, and x=0, and the perturbed term q:(0,1)→[0,+∞) is Lebesgue integrable and may have finitely many singularities in (0,1), which implies that the nonlinear term may change sign.…”
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MULTI-OBJECTIVE ROBUST OPTIMIZATION DESIGN OF COMPLIANT HINGE BASED ON BP NEURAL NETWORK (MT) by WU JianJun, LI JiaHui

“…Orthogonal experiments are used to select training parameters and test parameters, a BP neural network model is established, and by using the nonlinear fitting ability of the neural network and the global search and optimization ability of genetic algorithm. …”
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An Intelligence Optimized Rolling Grey Forecasting Model Fitting to Small Economic Dataset by Li Liu, Qianru Wang, Ming Liu, Lian Li

“…Grey system theory has been widely used to forecast the economic data that are often highly nonlinear, irregular, and nonstationary. The size of these economic datasets is often very small. …”
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Moving mesh simulations of pitting corrosion by Abu Naser Sarker, Ronald D. Haynes, Michael D. Robertson

“…The adaptive mesh is generated automatically by solving a mesh PDE coupled to the nonlinear potential problem. The moving mesh approach is shown to enable initial mesh generation, provide automatic mesh adjustment (or recovery) and is able to smoothly tackle changing pit geometry. …”
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The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations by Hassan A. Zedan, Eman El Adrous

“…HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZE equations and the approximate solutions, comparison of the HPM results with those of Adomian’s decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZE equations with the HPM solutions and HAM solutions are presented.…”
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The role of multiple modeling perspectives in students' learning of exponential growth by Carlos Castillo-Garsow

“…In order to investigate these issues, I preformed a teaching experiment with two high school students, which focused on building understandings of exponential growth leading up to the (nonlinear) logistic differential equation model. In this paper, I highlight some of the ways of thinking used by participants in this teaching experiment. …”
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A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics by Saima Akram, Faiza Akram, Moin-ud-Din Junjua, Misbah Arshad, Tariq Afzal

“…In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. …”
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Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays by Adsadang Himakalasa, Suttida Wongkaew

“…Furthermore, the Runge–Kutta discretization method and the nonlinear conjugate gradient method are employed to solve the discrete optimality system. …”
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The Influence of the Track Parameters on Vibration Characteristics of Subway Tunnel by Wenbo Shi, Linchang Miao, Junhui Luo, Honglei Zhang

“…In soft soil areas, such as the Nanjing, it is very important to quantitatively analyze the dynamic behaviors of soft soils during the metro train operation. A nonlinear coupling model of wheel-track and a finite element calculation model of tunnel and soil were established based on the mechanical character of elastic supporting block ballastless track and the actual parameters of Nanjing soft soil. …”
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On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells by Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel

“…The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. …”
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Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model by Fabien Crauste

“…We analyze the asymptotic stability of a nonlinear system of two differential equations with delay,describing the dynamics of blood cell production. …”
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Velocity Control for Coning Motion Missile System Using Direct Discretization Method by Rui-sheng Sun, Chao Ming

“…By using a direct discretization method to transform the optimal control problem into a nonlinear dynamic programming problem, the optimal trajectory and velocity profile are obtained to satisfy the design index requirement. …”
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Improved sliding mode temperature control of hydrogen fuel cells for multirotor drones by Qi Wu, Yong Zhang, Tingting Ru, Chenxiao Cai

“…The study focuses on constructing a control-oriented nonlinear thermal model, which serves as a foundation for the subsequent development of a practical temperature regulation approach. …”
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Further Results about Traveling Wave Exact Solutions of the Drinfeld-Sokolov Equations by Fu Zhang, Jian-ming Qi, Wen-jun Yuan

“…The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all constant and simply periodic traveling wave exact solutions of the equations (DS) are solitary wave solutions, the complex method is simpler than other methods and there exist simply periodic solutions vs,3(z) which are not only new but also not degenerated successively by the elliptic function solutions. …”
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Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method by Desmond Adair, Askar Ibrayev, Alima Tazabekova, Jong R. Kim

“…Important to the use of the Adomian modified decomposition method is the treatment of the nonlinear Fredholm integral coefficient, which forms part of the governing equation. …”
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Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods by F. Soleymani, S. Shateyi

“…Due to this, the main aim of this paper is to attain as high as possible of local convergence order by using fixed number of (functional) evaluations to find efficient solvers for one-variable nonlinear equations, while the procedure to achieve this goal is totally free from derivative. …”
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Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost by S. S. Askar, Ahmed M. Alshamrani

“…In this paper, some mathematical properties and dynamic investigations of a Cournot–Bertrand duopoly game using a computed nonlinear cost are studied. The game is repeated and its evolution is presented by noninvertible map. …”
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Bundle Pricing Decisions for Fresh Products with Quality Deterioration by Yan Fang, Yiping Jiang, Xingxing Han

“…The value of fresh products with quality deterioration is approximated as an exponential function based on which customer’s reservation prices are calculated. A nonlinear mixed integer programming model is used to formulate the bundle pricing problem for fresh products. …”
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