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Higher order derivative-free iterative methods with and without memory for systems of nonlinear equations

Author

Listed:
  • Ahmad, F.
  • Soleymani, F.
  • Khaksar Haghani, F.
  • Serra-Capizzano, S.

Abstract

A derivative-free family of iterations without memory consisting of three steps for solving nonlinear systems of equations is brought forward. Then, the main aim of the paper is furnished by proposing several novel schemes with memory possessing higher rates of convergence. Analytical discussions are reported and the theoretical efficiency of the methods is studied. Application of the schemes in solving partial differential equations is finally provided to support the theoretical discussions.

Suggested Citation

  • Ahmad, F. & Soleymani, F. & Khaksar Haghani, F. & Serra-Capizzano, S., 2017. "Higher order derivative-free iterative methods with and without memory for systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 199-211.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:199-211
    DOI: 10.1016/j.amc.2017.07.012
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    References listed on IDEAS

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    1. Ullah, Malik Zaka & Serra-Capizzano, S. & Ahmad, Fayyaz & Al-Aidarous, Eman S., 2015. "Higher order multi-step iterative method for computing the numerical solution of systems of nonlinear equations: Application to nonlinear PDEs and ODEs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 972-987.
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    Cited by:

    1. Cordero, Alicia & Leonardo-Sepúlveda, Miguel A. & Torregrosa, Juan R. & Vassileva, María P., 2024. "Increasing in three units the order of convergence of iterative methods for solving nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 509-522.
    2. Mozafar Rostami & Taher Lotfi & Ali Brahmand, 2019. "A Fast Derivative-Free Iteration Scheme for Nonlinear Systems and Integral Equations," Mathematics, MDPI, vol. 7(7), pages 1-11, July.

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