Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0) by Jing Li

“…The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. …”
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Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface by Atta Sojoudi, Ali Mazloomi, Suvash C. Saha, Y. T. Gu

“…Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. …”
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Variational Iteration Method of Dropping Shock Response for the Suspension Spring Packaging System by Shuang Song, An-Jun Chen

“…In accordance with dropping shock dimensionless cubic nonlinear dynamic equation of suspension spring system, by variational iteration method, a first-order approximate solution of the system was obtained. …”
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A Normal Contact Stiffness Statistical Model of Joint Interface considering Hardness Changes by Donghua Yin, Xueliang Zhang, Shuhua Wen, Guosheng Lan, Yonghui Chen

“…The simulation results show that the normal contact stiffness of joint interface is a nonlinear function of the mean surface separation and decreases with the increase of the mean surface separation under different plasticity indexes. …”
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Topological Quasilinear Spaces by Yılmaz Yılmaz, Sümeyye Çakan, Şahika Aytekin

“…He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. …”
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A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity by S. Shateyi, G. T. Marewo

“…A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. The resultant ordinary differential equations are then solved using a successive relaxation method (SRM). …”
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Least Square Homotopy Perturbation Method for Ordinary Differential Equations by Mubashir Qayyum, Imbsat Oscar

“…The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. …”
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On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances by T. S. Amer, M. A. Bek, I. S. Hamada

“…The response of a nonlinear multidegrees of freedom (M-DOF) for a nature dynamical system represented by a spring pendulum which moves in an elliptic path is investigated. …”
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A Numerical Solution for Hirota-Satsuma Coupled KdV Equation by M. S. Ismail, H. A. Ashi

“…Newton’s method is used to solve the block nonlinear pentadiagonal system we have obtained. The resulting schemes are of second order accuracy in both directions, space and time. …”
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An Index for Measuring Functional Diversity in Plant Communities Based on Neural Network Theory by Naiqi Song, Jin-Tun Zhang

“…The results showed that SOFM index was an effective method in the evaluation of functional diversity and its change in plant communities. Significant nonlinear correlations of SOFM index with the common used methods, FAD, MFAD, FDp, FDc, FRic, and FDiv indices, also proved that SOFM index is useful in the studies of functional diversity.…”
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Proportional PDC Design-Based Robust Stabilization and Tracking Control Strategies for Uncertain and Disturbed T-S Model by Chekib Ghorbel, Amira Tiga, Naceur Benhadj Braiek

“…This paper presents a proportional parallel distributed compensation (PPDC) design to the robust stabilization and tracking control of the nonlinear dynamic system, which is described by the uncertain and perturbed Takagi–Sugeno (T-S) fuzzy model. …”
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Wavelet Optimal Estimations for Density Functions under Severely Ill-Posed Noises by Rui Li, Youming Liu

“…Then, we prove a lower bound, which shows our wavelet estimator optimal. In other words, nonlinear wavelet estimations are not needed in that case. …”
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Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid by Norihan Md. Arifin, Roslinda Nazar, Ioan Pop

“…The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. …”
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Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…The linear part of the equations is assumed to generate a compact analytic semigroup of bounded linear operators, whereas the nonlinear part satisfies the Carathëodory condition and is bounded by some suitable functions. …”
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Hydrodynamic scaling limit of continuum solid-on-solid model by Anamaria Savu

“…A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. …”
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Dynamic Modeling and Optimal Control for Complex Systems with Statistical Trajectory by Lingli Guo, Zhengguang Xu, Ye Wang

“…Firstly, a novel discrete-time nonlinear working state class dynamic mathematical model of sintering machine is constructed by K-means cluster method for the local data, which overcomes difficulties of modeling by mechanism and describes the class change against the point movement. …”
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Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge by Juan Li, Yongzhong Song, Hui Wan, Huaiping Zhu

“…Bifurcation analyses are given by using normal form theory which reveals reasonably the mechanisms and nonlinear dynamics of the effects of toxin and refuges, including Hopf bifurcation, Bogdanov-Takens bifurcation of co-dimension 2 and 3. …”
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Impact Force Magnitude Analysis of an Impact Pendulum Suspended in a Vibrating Structure by R.R. Aguiar, H.I. Weber

“…The mathematical model allows a detailed nonlinear analysis, showing the rich response of the system, which includes dynamical jumps, bifurcations and chaos. …”
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Spatiotemporal Dynamics of a Delayed Viral Infection Model with Two Modes of Transmission and Immune Impairment by Hui Miao, Meiyan Jiao

“…In this paper, the dynamical behaviors for a diffusive virus infection model with two general nonlinear incidence functions, CTL immune impairment and discrete delays, are investigated. …”
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Modeling and Estimation of Thermal Flows Based on Transport and Balance Equations by Angelo Alessandri, Patrizia Bagnerini, Roberto Cianci, Roberto Revetria

“…Toward this end, a method to construct nonlinear Lyapunov functionals is addressed by relying on a polynomial diagonal structure. …”
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