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Hybrid approximations via second order combined dynamic derivatives on time scales [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2007 This article focuses on the approximation of conventional second order derivative via the combined (diamond-$\alpha$) dynamic derivative on time scales with necessary smoothness conditions embedded.
Qin Sheng
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High order second derivative diagonally implicit multistage integration methods for ODEs
Mathematical Modelling and Analysis, 2023 Construction of second derivative diagonally implicit multistage integration methods (SDIMSIMs) as a subclass of second derivative general linear methods with Runge–Kutta stability property requires to generate the corresponding conditions depending of ...
Mohammad Sharifi +3 more
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Second Derivative Block Hybrid Methods for the Numerical Integration of Differential Systems
Fractal and Fractional, 2022 The second derivative block hybrid method for the continuous integration of differential systems within the interval of integration was derived. The second derivative block hybrid method maintained the stability properties of the Runge–Kutta methods ...
Dauda Gulibur Yakubu +3 more
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Mathematics, 2023 This research aims to propose a new family of one-parameter multi-step iterative methods that combine the homotopy perturbation method with a quadrature formula for solving nonlinear equations. The proposed methods are based on a higher-order convergence
Huda J. Saeed +4 more
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Barekeng, 2022 The variant of Chebyshev-Halley’s method is an iterative method used for solving a nonlinear equation with third order of convergence. In this paper, we present some new variants of three steps Chebyshev-Halley’s method free from second derivative with ...
Yuslenita Muda +3 more
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High order second derivative methods with Runge--Kutta stability for the numerical solution of stiff ODEs [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2015 We describe the construction of second derivative general linear methods (SGLMs) of orders five and six. We will aim for methods which are A--stable and have Runge--Kutta stability property. Some numerical results are given to show the efficiency of
Ali Abdi, Gholamreza Hojjati
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Journal of Telecommunications and Information Technology, 2023 The paper presents an idea to use weak derivatives in interval global optimization. It allows using the Newton operator to narrow domains of non-differentiable functions. Preliminary computational experiments are also presented.
Bartłomiej Jacek Kubica
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Polynomial Formulation of Second Derivative Multistep Methods [PDF]
Mathematics of Computation, 1982 Following the work of Enright [3] there has been interest in studying second derivative methods for solving stiff ordinary differential equations. Successful implementations of second derivative methods have been reported by Enright [3], Sacks-Davis [9], [10] and Addison[l].
Kovvali, S., Gupta, G. K.
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Second derivative General Linear Method in Nordsieck form
Journal of Numerical Analysis and Approximation Theory, 2019 This paper considers the construction of second derivative general linear methods (SD-GLM) from hybrid LMM and their transformation to Nordsieck GLM. How the Runge-Kutta starters for the methods can be derived are given.
Robert I. Okuonghae +1 more
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Symmetric second derivative integration methods
Journal of Computational and Applied Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hosseini Nasab, M. +2 more
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