Renormalization group analysis for thermal turbulence by D. N. Riahi

“…Turbulent fluxes for the flow are accounted for by repeatedly recasting the governing equations with the smallest scales represented by effective larger scales. Expressions for nonlinear contributions to eddy viscosity and eddy diffusivity are determined, and leading order contributions due to buoyancy on various results and equations are estimated. …”
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A Modified Hybrid Conjugate Gradient Method for Unconstrained Optimization by Minglei Fang, Min Wang, Min Sun, Rong Chen

“…The nonlinear conjugate gradient algorithms are a very effective way in solving large-scale unconstrained optimization problems. …”
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An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces by H. Zegeye, N. Shahzad

“…Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.…”
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Investigation of Cracking in Reinforced Concrete Structures by Means of Standardized Deformation Models by Mikhail V. Morgunov, Anzhelika A. Lyudkevich

“…For theoretical verification of the values of the moment of cracking, calculation methods based on the use of a nonlinear deformation model are used.A theoretical study of cracking moment using a non-linear deformation model shows that the application of a two-line diagram of concrete deformation allows to obtain the most accurate values of cracking moment.…”
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Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form by Abdelrady Okasha Elnady, M. Fayek Abd Rabbo, Hani M. Negm

“…A numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the Chebyshev series. …”
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Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator by Sombir Dhaniya, Anoop Kumar, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah

“…In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. …”
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On Positive Radial Solutions for a Class of Elliptic Equations by Ying Wu, Guodong Han

“…A class of elliptic boundary value problem in an exterior domain is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where the variables of nonlinear term fs,u need not to be separated. Several new theorems on the existence and multiplicity of positive radial solutions are obtained by means of fixed point index theory. …”
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Global Stability of a Rational Difference Equation by Guo-Mei Tang, Lin-Xia Hu, Gang Ma

“…We consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers. …”
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Pricing Option with Stochastic Interest Rates and Transaction Costs in Fractional Brownian Markets by Lina Song, Kele Li

“…By the means of the hedging and replicating techniques, the new equations satisfied by zero-coupon bond and the nonlinear equation obeyed by European option are established in succession. …”
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Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function by A. X. Martins, R. A. S. Paiva, G. Petronilo, R. R. Luz, R. G. G. Amorim, S. C. Ulhoa, T. M. R. Filho

“…In this work, we study symplectic unitary representations for the Galilei group. As a consequence a nonlinear Schrödinger equation is derived in phase space. …”
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The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation by Nan Li, Shaoyong Lai, Shuang Li, Meng Wu

“…A nonlinear generalization of the Camassa-Holm equation is investigated. …”
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A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation by Liquan Mei, Yali Gao, Zhangxin Chen

“…In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. …”
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The Estimate for Approximation Error of Neural Network with Two Weights by Fanzi Zeng, Yuting Tang

“…We prove that it can limitlessly approach any continuous function from limited close subset of Rm to Rn and any continuous function, which has limit at infinite place, from limitless close subset of Rm to Rn. This extends the nonlinear approximation ability of traditional BP neural network and RBF neural network.…”
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Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials by Syed Tauseef Mohyud-Din, Ahmet Yildirim, M. M. Hosseini

“…The elegant coupling gives rise to the modified versions of VIM which is very efficient in solving nonlinear problems of diversified nature. It is observed that the variational iteration method using He's polynomials (VIMHP) is very efficient, easier to implements, and more user friendly. …”
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Qualitative Analysis of Coating Flows on a Rotating Horizontal Cylinder by Marina Chugunova, Roman M. Taranets

“…We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of gravity. …”
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Actuator Fault Diagnosis in a Boeing 747 Model via Adaptive Modified Two-Stage Kalman Filter by Fikret Caliskan, Youmin Zhang, N. Eva Wu, Jong-Yeob Shin

“…An adaptive modified two-stage linear Kalman filtering algorithm is utilized to identify the loss of control effectiveness and the magnitude of low degree of stuck faults in a closed-loop nonlinear B747 aircraft. Control effectiveness factors and stuck magnitudes are used to quantify faults entering control systems through actuators. …”
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Existence Results of Nonlocal Fractional Integro-Neutral Differential Inclusions with Infinite Delay by Madeaha Alghanmi, Shahad Alqurayqiri

“…Then, sufficient criteria for the existence of solutions are established for the convex case of the given problem using the nonlinear Leray–Schauder alternative type, while Covitz and Nadler’s theorem is applied for nonconvex multivalued functions. …”
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A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind by Lie-jun Xie

“…The validity and applicability of the new technique are illustrated through several linear and nonlinear equations by comparing with the standard decomposition method and the modified decomposition method. …”
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Mean Square Exponential Stability of Stochastic Cohen-Grossberg Neural Networks with Unbounded Distributed Delays by Chuangxia Huang, Lehua Huang, Yigang He

“…This paper addresses the issue of mean square exponential stability of stochastic Cohen-Grossberg neural networks (SCGNN), whose state variables are described by stochastic nonlinear integrodifferential equations. With the help of Lyapunov function, stochastic analysis technique, and inequality techniques, some novel sufficient conditions on mean square exponential stability for SCGNN are given. …”
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Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation by Ting Zhang, Chun Shen

“…For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. …”
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