Fired Heaters Optimization by Estimating Real-Time Combustion Products Using Numerical Methods by Ricardo Sánchez, Argemiro Palencia-Díaz, Jonathan Fábregas-Villegas, Wilmer Velilla-Díaz

“…Thermochemical data are used to calculate equilibrium constants as a function of temperature, with the least squares method, while the Newton–Raphson method solves the resulting nonlinear equations. …”
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Numerical benchmarking of dual decomposition-based optimization algorithms for distributed model predictive control by Vassilios Yfantis, Achim Wagner, Martin Ruskowski

“…Finally, the quasi-Newton dual ascent algorithm is compared to the subgradient method, the bundle trust method and the alternating direction method of multipliers for a large number of benchmark problems. …”
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The Hessian by blocks for neural network by backward propagation by Radhia Bessi, Nabil Gmati

“…Newton's method offers potential advantages in terms of faster convergence. …”
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Quadrature based innovative techniques concerning nonlinear equations having unknown multiplicity by Farooq Ahmed Shah, Muhammad Waseem

“…The derived methods are the variants of modified Newton method with high order of convergence and better accuracy. …”
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Parallel Jacobian Computation Based on Distance-2 Algorithm and Its Application in Coupling Problems by LIU Lixun, ZHANG Han, PENG Xinru, DOU Qinrong, WU Yingjie, GUO Jiong, LI Fu

“…The fission nuclear reactor is a typical complicated multi-physics coupling system because of the nonlinear coupled terms among different physical fields. The Newton-Krylov method is an effective method for solving the multi-physics coupling problem, featuring strong stability and a high-order convergence rate. …”

A novel Bessel–Newton algorithm for the simulation of 2D laminar flow between two moving porous walls problem by Atallah El-shenawy, Mohamed El-Gamel, Muhammad E. Anany

“…We propose a unique Bessel–Newton algorithm that utilizes the Bessel operational matrices collocation method for discretizing the equations and employs a Newton iterative strategy to resolve the resulting nonlinear system. …”
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Control-Oriented Free-Boundary Equilibrium Solver for Tokamaks by Xiao Song, Brian Leard, Zibo Wang, Sai Tej Paruchuri, Tariq Rafiq, Eugenio Schuster

“…Additionally, the proposed solver was benchmarked against another numerical solver based on the finite-element and Newton-iteration methods in a triangular-based mesh. …”
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Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering by M. A. Rehman, Amir Naseem, Thabet Abdeljawad

“…We develop these iteration schemes with the help of Taylor’s series expansion, generalized Newton-Raphson’s method, and interpolation technique. …”
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IMPROVED ALGORITHM FOR QUASI-STATIC SOLUTION OF HIGH SPEED ANGULAR CONTACT BALL BEARING by GAO Feng, HE PingPing, LI Yan, SHUI LinQi

“…Firstly,the intermediate variables are introducd to reduce the number of unknowns and the nonlinear equations are solved with step algorithm by which it’s ease to select the initial value. Secondly,the iterative correction factor optimized by bisection method is used to improve NewtonRaphson algorithm by which the convergence time is shortened. …”
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Super class of implicit extended backward differentiation formulae for the numerical integration of stiff initial value problems by Hamisu Musa, Buhari Alhassan

“…The SEBDF schemes are implemented using a Modified Newton iteration algorithm iterated to convergence in which some selected systems of first-order stiff IVPs are solved, and the numerical results obtained for the proposed methods are often better than the existing BDF and SBDF methods for solving stiff IVPs.…”
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The Hybrid BFGS-CG Method in Solving Unconstrained Optimization Problems by Mohd Asrul Hery Ibrahim, Mustafa Mamat, Wah June Leong

“…In solving large scale problems, the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. …”
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A Midcourse Guidance Method Combined with Trajectory Prediction for Antinear-Space-Gliding Vehicles by JiaQing Wan, Qian Zhang, Hao Zhang, JiaNing Liu

“…For the calculation of the starting time of the boost phase, the optimization solution satisfying the remaining flight time constraint is realized based on the Newton-Raphson iterative method. The analytical expression of a guidance command based on zero-error-miss/zero-error-velocity is established on the basis of the optimal control theory to provide an optimal flight path guiding an NSGV fly toward a point of interception. …”
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An Efficient Modified AZPRP Conjugate Gradient Method for Large-Scale Unconstrained Optimization Problem by Ahmad Alhawarat, Thoi Trung Nguyen, Ramadan Sabra, Zabidin Salleh

“…To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. …”
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A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation by Fiza Zafar, Nusrat Yasmin, Saima Akram, Moin-ud-Din Junjua

“…We construct a new general class of derivative free n-point iterative methods of optimal order of convergence 2n-1 using rational interpolant. …”
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An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers by John Machacek, Shafiu Jibrin

“…The algorithm uses Newton’s method to compute the weighted analytic center. …”
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Enlarged current injection model for the power flow solution of unbalanced distribution networks by Rubén Carmona-Pardo, Álvaro Rodríguez del Nozal, Esther Romero-Ramos, Antonio Gómez-Expósito

“…The proposed formulation uses rectangular coordinates and, unlike most earlier approaches, both bus voltages and injected currents are retained as variables. The Newton–Raphson method is then applied to the augmented system of equations, resulting in an iterative process that is solved optimally. …”
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GENERAL MODEL AND STABILITY STUDY OF CYLINDIRCAL GRINDING CHATTER (MT) by CHI YuLun, LIU Bin, SHEN YiFeng

“…The overlapping factor related to the width of the grinding wheel was introduced into the general dynamic model to fully consider the regenerative chatter relationship between the workpiece and the grinding wheel, and it can be used in longitudinal grinding and circular cutting grinding. In this model, Newton iterative method was used to solve the transcendental equation with time delay, Gaussian elimination method was used to improve the iterative convergence speed, the continuation algorithm was used to continuously provide effective initial values to improve the accuracy of the iterative results, and the accurate grinding stability boundary was obtained. …”
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New Fractional Derivative Expression of the Shifted Third-Kind Chebyshev Polynomials: Application to a Type of Nonlinear Fractional Pantograph Differential Equations by Y. H. Youssri, W. M. Abd-Elhameed, H. M. Ahmed

“…To solve a nonlinear fractional pantograph differential equation with quadratic nonlinearity, the fractional derivative formula is used in conjunction with the tau technique. The role of the tau method is to convert the pantograph differential equation with its governing initial/boundary conditions into a nonlinear system of algebraic equations that can be treated with the aid of Newton’s iterative scheme. …”
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ISI sparse channel estimation based on ISL0 algorithm by Ting LIU, Jie ZHOU, CHIJiu-he JU

“…Moreover, the “steep nature” of cost function in SL0 is not steep enough, leading to channel estimation errors and make convergence results not the most optimal. The lagrange multipliers and newton method were combined to op-timize SL0 algorithm in order to obtain a more rapid and efficient signal reconstruction algorithm termed as an improved smoothed L0 (ISL0). …”
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Optimization Control of Cooperative Trajectory towards Dual Arms Based on Time-Varying Constrained Output State by Hui Zhang, Wenbin Zha, Xiangrong Xu, Yongfei Zhu

“…Using random probability distribution to extract the interpolation features of nonuniform quintic B-spline trajectory, the feature optimization target is selected, and the Newton numerical algorithm is used for iterative optimization. …”
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