Perihelion Precessions of Inner Planets in Einstein’s Theory and Predicted Values for the Cosmological Constant by Alvaro H. Salas S, Jairo E Castillo H, Lorenzo J. Martınez H

“…In this paper, we obtain the approximate value of 42.9815 arcsec/century for Mercury’s perihelion precession by solving both numerically and analytically the nonlinear ordinary differential equation derived from the geodesic equation in Einstein’s Theory of Relativity. …”
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Sumudu residual power series method to solve time-fractional Fisher’s equation by Rajendra Pant, Geeta Arora, Homan Emadifar, Ahmed A. Hamoud

“…In this paper, the one-dimensional nonlinear temporal fractional-order Fisher’s equation is solved by using the Sumudu residual power series method (SRPSM), a powerful computing technique. …”
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A graphical exploration of the relationship between parasite aggregation indices. by R McVinish, R J G Lester

“…The contour plots highlight the nonlinear nature of the relationships between these measures and suggest that correlations are not a suitable summary of these relationships.…”
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Applications of Fuzzy Sliding Mode Control for a Gyroscope System by Shih-Chung Chen, Chao-Lin Kuo, Chia-Hung Lin, Chih-Hung Hsu, Chien-Kuo Tsui

“…The state response analysis of the gyroscope system revealed highly nonlinear and chaotic subharmonic motions of 2T during state formation. …”
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Real-Time Trajectory Planning and Control for Constrained UAV Based on Differential Flatness by Dongli Wu, Hao Zhang, Yunping Liu, Weihua Fang, Yan Wang

“…A differential flat theory based on B-spline trajectory planning can replace the optimal control problem with nonlinear programming and be a good means to achieve the efficient trajectory planning of an UAV under multiple dynamic constraints. …”
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Complete Solutions to General Box-Constrained Global Optimization Problems by Dan Wu, Youlin Shang

“…This paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. …”
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A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations by Alicia Cordero, José L. Hueso, Eulalia Martínez, Juan R. Torregrosa

“…A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. …”
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Optimum Design of Multidischarge Outlet Biomass Briquetting Machine by Jiaqi Yang, Jirong Wang, Jun Li, Lianwen Shi, Xiangwu Dai

“…To further improve efficiency and rationally allocate power at each stage, in this paper, we established a mathematical model for the machine. We use the nonlinear programming in Matlab (2016b) to solve the minimum value of the model, making the machine work time the shortest.…”
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Analytical Solutions of Time-Fractional Navier–Stokes Equations Employing Homotopy Perturbation–Laplace Transform Method by Awatif Muflih Alqahtani, Hamza Mihoubi, Yacine Arioua, Brahim Bouderah

“…The results show that the proposed method is robust, efficient, and easy to implement for both linear and nonlinear problems in science and engineering. Additionally, its computational efficiency requires less computation compared to other schemes.…”
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Existence of Solutions for Singular Second-Order Ordinary Differential Equations with Periodic and Deviated Nonlocal Multipoint Boundary Conditions by Ahmed M. A. El-Sayed, Fatma M. Gaafar

“…This paper studies the existence of continuous solutions for a class of nonlinear singular second-order ordinary differential equations subject to one of the following boundary conditions: periodic-deviated multipoint boundary conditions, periodic-integral boundary conditions, and periodic-nonlocal integral conditions in the Riemann-Stieltjes sense. …”
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Homotopy Series Solutions to Time-Space Fractional Coupled Systems by Jin Zhang, Ming Cai, Bochao Chen, Hui Wei

“…The HPSTM is a combination of Sumudu transform and homotopy perturbation method, which can be easily handled with nonlinear coupled system. We apply the method to the coupled Burgers system, the coupled KdV system, the generalized Hirota-Satsuma coupled KdV system, the coupled WBK system, and the coupled shallow water system. …”
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An optimal energy-efficient resource allocation algorithm in ultra-dense network by Yueyue ZHANG, Weiwei XIA, Yaping ZHU, Feng YAN, Xuzhou ZUO, Lianfeng SHEN

“…The energy-efficient resource allocation problem was taken in an ultra-dense network(UDN) consisted of multiple femtocells.Aiming at maximizing the energy efficiency (EE) of the whole network,quality of service (QoS) constraint and interference limitation was considered.Then,the established nonconvex and nonlinear problem was relaxed relying on Cauchy inequality,and was developed into a non-cooperative game.Additionally,a distributed EE maximization algorithm was proposed satisfying the max-min fairness (MMF) criterion.Simulation results show that the proposed algorithm outperformances the existing algorithms in terms of the EE and the throughput.…”
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Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods by Yongyi Gu, Fanning Meng

“…The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.…”
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Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate by Yongli Cai, Xixi Wang, Weiming Wang, Min Zhao

“…We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. …”
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Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis by N. Mindu, D. P. Mason

“…The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. …”
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Discrete Dynamics in Evolutionary Games by Orlando Gomes

“…Evolutionarily stable strategies are identified and nonlinear outcomes are explored. Besides the baseline payoffs of the established strategic interaction, the following elements are also vital to determine the dynamic outcome of a game: the initial fitness of each agent and the rule of motion that describes how individuals switch between strategies. …”
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Optimal Parametric Iteration Method for Solving Multispecies Lotka-Volterra Equations by Vasile Marinca, Nicolae Herişanu

“…This new approach, which can be easily applied to other strongly nonlinear problems, is very effective and yields very accurate results.…”
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Image Denoising Using Fourth Order Wiener Filter with Wavelet Quadtree Decomposition by Issam Dagher, Catherine Taleb

“…This paper uses the fourth order nonlinear wiener filter with wavelet quadtree decomposition and median absolute deviation. …”
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Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions by Tamás Kalmár-Nagy, Márton Kiss

“…Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. …”
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Weakly Coupled B-Type Kadomtsev-Petviashvili Equation: Lump and Rational Solutions by Na Xiong, Wen-Tao Li, Biao Li

“…This method of solving the lump and rational solutions can also be applied to other nonlinear evolution equations.…”
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