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New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns

Author

Listed:
  • Ramandeep Behl

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Alicia Cordero

    (Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 Valencia, Spain)

  • Juan R. Torregrosa

    (Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 Valencia, Spain)

  • Ali Saleh Alshomrani

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature.

Suggested Citation

  • Ramandeep Behl & Alicia Cordero & Juan R. Torregrosa & Ali Saleh Alshomrani, 2018. "New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns," Mathematics, MDPI, vol. 6(12), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:296-:d:187042
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    References listed on IDEAS

    as
    1. Khan, Waseem Asghar & Noor, Khalida Inayat & Bhatti, Kaleemulah & Ansari, Faryal Aijaz, 2015. "A new fourth order Newton-type method for solution of system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 724-730.
    2. Moin-ud-Din Junjua & Saima Akram & Nusrat Yasmin & Fiza Zafar, 2015. "A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-14, March.
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