Article
A composite third order Newton–Steffensen method for solving nonlinear equations
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, 148 106 District Sangrur, India
Applied Mathematics and Computation (Impact Factor: 1.35). 01/2005; DOI: 10.1016/j.amc.2004.10.040 Source: DBLP

Conference Paper: A Modified NewtonType Method with SixthOrder Convergence for Solving Nonlinear Equations.
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ABSTRACT: In this paper, we present and analyze a sixthorder convergent method for solving nonlinear equations. The method is free from second derivatives and permits f’(x)=0 in some points. It requires three evaluations of the given function and two evaluations of its derivative in each step. Some numerical examples illustrate that the presented method is more efficient and performs better than classical Newton’s method.Advances in Computer Science, Environment, Ecoinformatics, and Education  International Conference, CSEE 2011, Wuhan, China, August 2122, 2011. Proceedings, Part IV; 01/2011  [Show abstract] [Hide abstract]
ABSTRACT: We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable conditions on the monotony and convexity of the nonlinear function, the iterations offer bilateral approximations for the solution, which can be efficiently used as a posteriori estimations.Applied Mathematics and Computation 02/2011; 217(12):5838–5846. · 1.35 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, a new approach is presented to accelerate the nonlinear analysis of structures with low computational cost. The method is essentially based on Newton–Raphson method, which has been improved in each iteration to achieve faster convergence. The normal flow algorithm has been employed to pass successfully through the limit points and through the entire equilibrium path. Subsequently, numerical examples are performed to demonstrate the efficiency of the formulation. The results show better performance, accuracy and rate of convergence of the present method to deal with nonlinear analysis of structures.International Journal of Computational Methods 08/2013; 10(4). · 0.48 Impact Factor
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