Modification of the Quasilinearization Method for the Inverse Problem by Lenka Celechovská-Kozáková

“…We propose a new modification of Bellman's quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parameters α(k+1) which are close enough to the previous ones. …”
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Global stability of equilibria in a tick-borne disease model by Shangbing Ai

“…In this short note we establish global stability results for afour-dimensional nonlinear system that was developed in modeling atick-borne disease by H.D. …”
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Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model by Yacouba Simporé, Oumar Traoré

“…We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. …”
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Parameter estimation in a structured erythropoiesis model by Azmy S. Ackleh, Jeremy J. Thibodeaux

“…We develop a numerical method for estimating parameters in astructured erythropoiesis model consisting of a nonlinear system ofpartial differential equations. Convergence theory for the computedparameters is provided. …”
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Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments by Mahdi Namazi Nezamabadi, Saeed Pishbin

“…We also investigate solvability of the obtained nonlinear system with infinite dimensional space and examine the convergence analysis of this method under the L2− norm. …”
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Nonlinear elliptic problems with the method of finite volumes by Sanjay Kumar Khattri

“…Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.…”
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The Systems of Nonlinear Gradient Flows on Metric Spaces and Its Gamma-Convergence by Mao-Sheng Chang, Bo-Cheng Lu

“…This scheme is a nonlinear system edition of the notion initiated by Sylvia Serfaty in 2011.…”
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Global stability for the prion equation with general incidence by Pierre Gabriel

“…We consider the so-called prion equation with the general incidence term introduced in [14], and we investigate the stability of the steady states.The method is based on the reduction technique introduced in [11].The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.…”
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Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel by M. Taghipour, H. Aminikhah

“…For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative, nonlinear, and integro–differential terms; and by collocation points, we transform the problem to a system of nonlinear equations. This nonlinear system can be solved by the fsolve command in Matlab. …”
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The Dynamic Three-Dimensional Localization of Fields in Active Percolating Systems by Gennadiy Burlak

“…Our numerical 3D simulations show that such a nonlinear system with noninteger fractal dimension has well-defined localized solutions for fields (3D speckles). …”
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Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks by Van Truong Vo, Samad Noeiaghdam, Denis Sidorov, Aliona Dreglea, Liguo Wang

“…Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. …”
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Algorithms for Solving the Equilibrium Composition Model of Arc Plasma by Zhongyuan Chi, Yuzhang Ji, Ningning Liu, Tianchi Jiang, Xin Liu, Weijun Zhang

“…This model is essentially a nonlinear system of weakly singular Jacobian matrices. …”
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Self-organization in interface dynamics and urban development by Ehud Meron

“…The view of the urban environment as an extended nonlinear system introduces new concepts, motivates new questions, and suggests new methodologies in the study of urban dynamics. …”
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Two-Phase Generalized Reduced Gradient Method for Constrained Global Optimization by Abdelkrim El Mouatasim

“…In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. In the Optimization Phase, optimality is improved by means of the consideration of the objective function, on the tangent subspace to the constraints. …”
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A Note on Practical Stability of Nonlinear Vibration Systems with Impulsive Effects by Qishui Zhong, Hongcai Li, Hui Liu, Juebang Yu

“…This paper addresses the issue of vibration characteristics of nonlinear systems with impulsive effects. By utilizing a T-S fuzzy model to represent a nonlinear system, a general strict practical stability criterion is derived for nonlinear impulsive systems.…”
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A New Simultaneous Identification of the Harmonic Excitations and Nonlinear Damping of Forced Damped Nonlinear Oscillations: A Parametric Approach by T. S. Jang

“…In addition to the mathematical analysis, a numerical example involving a highly nonlinear system is examined for demonstrating the workability of the proposed method for simultaneously identifying both the two aforementioned excitations and nonlinear damping.…”
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Control of Nonlinear Distributed Parameter Systems Based on Global Approximation by Chunyan Du, Guansheng Xing

“…We extend an iterative approximation method to nonlinear, distributed parameter systems given by partial differential and functional equations. The nonlinear system is approached by a sequence of linear time-varying systems, which globally converges in the limit to the original nonlinear systems considered. …”
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Global Asymptotic Stability of Nonlinear Strict Feedback System via Backstepping Control Approach by Suka Garagara Kinwi, Stephen Ekwueme Aniaku, Christopher Chukwuma Asogwa, Emmanuel Chukwudi Mbah

“…The design of controller for nonlinear system in strict feedback form in which the equilibrium point is the origin is the focus of the study. …”
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Nonlinear Attitude and Altitude Trajectory Tracking Control of a Bicopter UAV in Geometric Framework by Vijay Reddy Vundela, Vijay Muralidharan

“…A geometric nonlinear attitude and altitude tracking controller is developed for the Bicopter and the asymptotic stability analysis is performed using the Lyapunov method for the closed-loop nonlinear system. The performance of the proposed altitude and attitude stabilization controller is validated through experimental hardware developed in-house. …”
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A Fourth Order Finite Difference Method for the Good Boussinesq Equation by M. S. Ismail, Farida Mosally

“…Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. …”
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