Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems

For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2017-01, Vol.2017 (2017), p.1-11
Main Authors: Cordero, Alicia, Torregrosa, Juan R., Gómez, Esther
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applied mathematics
Complex systems
Computing time
Conduction
Conduction heating
Conductive heat transfer
Efficiency
Heat
Heat transfer
Iterative methods
Iterative methods (Mathematics)
Methods
Nonlinear systems
Numerical analysis
Numerical methods
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Summary:For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the presented schemes.
ISSN:1076-2787
1099-0526
DOI:10.1155/2017/6457532