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Research on a Modified Newton-Type Method with Fifth-Order Convergence for Solving Nonlinear Equations with Application in Material Science

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Advances in Computer Science, Intelligent System and Environment

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 104))

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Abstract

Numerical solution methods of nonlinear equation have very broad application prospect in materials science. In this paper, we present and analyze a fifth-order convergent method for solving nonlinear equations. The method is free from second derivatives and permits f’(x)=0 at some iteration points. Several numerical tests demonstrate that the sixth-order method given in this paper is more efficient and performs better than classical Newton’s method.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Heze University, 274015, Heze, China

    Han Li

  2. College of Mathematics and System Science, Taishan University, 271021, Tai’an, China

    Liang Fang

Authors
  1. Han Li
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  2. Liang Fang
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Editor information

Editors and Affiliations

  1. Wuhan Section, International Science & Education Researcher Association, Special No.1 Jiangxia Road of Wuhan, Wuhan, China

    David Jin

  2. Guangzhou Section, International Science & Education Researcher Association, No.144, Jinheng Road Jinbi Garden 85-1102 southern Road of Industry Avenue Haizhu District, Guangzhou, Guang Dong provience, China

    Sally Lin

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© 2011 Springer-Verlag Berlin Heidelberg

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Li, H., Fang, L. (2011). Research on a Modified Newton-Type Method with Fifth-Order Convergence for Solving Nonlinear Equations with Application in Material Science. In: Jin, D., Lin, S. (eds) Advances in Computer Science, Intelligent System and Environment. Advances in Intelligent and Soft Computing, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23777-5_7

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  • DOI: https://doi.org/10.1007/978-3-642-23777-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23776-8

  • Online ISBN: 978-3-642-23777-5

  • eBook Packages: EngineeringEngineering (R0)

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