Truncation error estimation for Newton–Cotes quadrature formulas by Kostas Plukas, Danutė Plukienė

“… Theoretical and practical aspects of truncation error estimation for Newton–Cotes quadrature formulas are discussed in this paper. …”
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An iterative method based on the average quadrature formula by Tusar Singh, Dwiti Behera, Shno Othman Ahmed, Rostam Saeed

“…The newly developed quadrature formula is then used to establish the new iterative scheme, which modifies the Newton-Raphson method. …”
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New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions by Jarunee Soontharanon, Muhammad Ali, Shahram Rezapour, Muhammad Toseef, Thanin Sitthiwirattham

Subjects: “…open newton-cotes formulas…”
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Midpoint Derivative-Based Closed Newton-Cotes Quadrature by Weijing Zhao, Hongxing Li

“…It is proved that these kinds of quadrature rules obtain an increase of two orders of precision over the classical closed Newton-Cotes formula, and the error terms are given. …”
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A Newton Interpolation Approach to Generalized Stirling Numbers by Aimin Xu

“…The generalizations of the well-known Dobinski's formula are further investigated.…”
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Improved Newton Iterative Algorithm for Fractal Art Graphic Design by Huijuan Chen, Xintao Zheng

“…Fractal art graphics are the product of the fusion of mathematics and art, relying on the computing power of a computer to iteratively calculate mathematical formulas and present the results in a graphical rendering. …”
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Numerical collocation technique for solving modified equal width wave equation by Aqib Zafar, Shyam Sundra Santra, Muhammad Nasir

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An innovative and efficient implementation of matrix-free Newton krylov method for neutronics/thermal-hydraulics coupling simulation by Peijun Li, Chen Hao, Ning Xu, Yanling Zhu, Yizhen Wang, Zhigang Zhang

“…In addition, the nonlinear preconditioning and hybrid perturbation size formula are implemented to further improve the convergence. …”
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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

“…An implicit Superclass of non-block Extended Backward Differentiation Formulae (SEBDF) for the numerical integration of first-order stiff system of Ordinary Differential Equations (ODEs) in Initial Value Problems (IVPs) with optimal stability properties is presented. …”
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Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems by L. Bergamaschi, A. Martínez

“…A sequence of preconditioners starting from an enhanced approximate inverse RFSAI (Bergamaschi and Martínez, 2012) and enriched by a BFGS-like update formula is proposed to accelerate the preconditioned conjugate gradient solution of the linearized Newton system to solve Au=q(u)u, q(u) being the Rayleigh quotient. …”
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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

“…The main goal of this paper is to develop a new formula of the fractional derivatives of the shifted Chebyshev polynomials of the third kind. …”
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Pseudo-Stieltjes calculus: $ \alpha- $pseudo-differentiability, the pseudo-Stieltjes integrability and applications by Caiqin Wang, Hongbin Xie, Zengtai Gong

“…In this paper, the concepts of the $ \alpha- $pseudo-differentiability and the pseudo-Stieltjes integrability are proposed, and the corresponding transformation theorems and Newton–Leibniz formula are established. The obtained results provide a framework for analyzing nonlinear differential equations.…”
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Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays by Manlika Rajchakit, Grienggrai Rajchakit

“…By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. …”
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Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type by W. Weera, P. Niamsup

“…By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. …”
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New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations by Sirada Pinjai, Kanit Mukdasai

“…Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). …”
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Companion of Ostrowski Inequality for Multiplicatively Convex Functions by Badreddine Meftah, Abdelghani Lakhdari, Saleh Wedad, Chemeseddine djaber Benchettah

“…Initially, we establish a novel identity using the two-point Newton-Cotes formula for multiplicatively differentiable functions. …”
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Delay-Range-Dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Fast Time-Varying Delays by Pin-Lin Liu

“…By developing delay decomposition approach, integral inequalities approach (IIA), and Leibniz-Newton formula, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. …”
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Guaranteed Cost Control for Exponential Synchronization of Cellular Neural Networks with Mixed Time-Varying Delays via Hybrid Feedback Control by T. Botmart, W. Weera

“…Based on the construction of improved Lyapunov-Krasovskii functionals is combined with Leibniz-Newton's formula and the technique of dealing with some integral terms. …”
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Estimation of stationary and non-stationary moving average processes in the correlation domain. by Martin Dodek, Eva Miklovičová

“…Unlike conventional methods, this approach uses the Newton-Raphson and Levenberg-Marquardt algorithms to efficiently find the solution. …”
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Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma by Dawei Gong, Frank L. Lewis, Liping Wang, Dong Dai, Shuang Zhang

“…First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. …”
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