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A novel fixed point iteration method for the solution of third order boundary value problems

Author

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  • Abushammala, Mariam
  • Khuri, S.A.
  • Sayfy, A.

Abstract

In this work, a new alternative uniformly convergent iterative scheme is presented and applied for the solution of an extended class of linear and nonlinear third order boundary value problems that arise in physical applications. The method is based on embedding Green’s functions into well-known fixed point iterations, including Picard’s and Krasnoselskii–Mann’s schemes. Convergence of the numerical method is proved by manipulating the contraction principle. The effectiveness of the proposed approach is established by implementing it on several numerical examples, including linear and nonlinear third order boundary value problems. The results show highly accurate approximations when compared to exact and existing numerical solutions.

Suggested Citation

  • Abushammala, Mariam & Khuri, S.A. & Sayfy, A., 2015. "A novel fixed point iteration method for the solution of third order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 131-141.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:131-141
    DOI: 10.1016/j.amc.2015.08.129
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    Cited by:

    1. Hui Zhang & Xin Cheng & Tinglin Huang & Haibing Cong & Jinlan Xu, 2017. "Hydraulic Analysis of Water Distribution Systems Based on Fixed Point Iteration Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(5), pages 1605-1618, March.
    2. Mohd Nasir, Nadirah & Abdul Majid, Zanariah & Ismail, Fudziah & Bachok, Norfifah, 2021. "Direct integration of the third-order two point and multipoint Robin type boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 411-427.

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