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Second Derivative Block Hybrid Methods for the Numerical Integration of Differential Systems [PDF]
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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Construction of Nordsieck Second Derivative General Linear Methods with Inherent Quadratic Stability
Mathematical Modelling and Analysis, 2017 This paper describes the construction of second derivative general linear methods in Nordsieck form with stability properties determined by quadratic stability functions. This is achieved by imposing the so–called inherent quadratic stability conditions.
Akram Movahedinejad +2 more
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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 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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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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One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems [PDF]
Journal of Applied MathematicsThis paper introduces a novel approach for solving first-order stiff initial value problems through the development of a one-step family of three optimized second-derivative hybrid block methods.
Saidu Daudu Yakubu, Precious Sibanda
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A class of explicit second derivative general linear methods for non-stiff ODEs
Mathematical Modelling and AnalysisIn this paper, we construct explicit second derivative general linear methods (SGLMs) with quadratic stability and a large region of absolute stability for the numerical solution of non-stiff ODEs.
Mohammad Sharifi +3 more
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Electronic Journal of Differential Equations, 2014 In this article, we study the existence of solutions for nonlinear impulsive problems. We show the existence of classical solutions by using variational methods.
Jian Liu, Zengqin Zhao
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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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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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