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Numerical Solution of Nonlinear Second Order Singular BVPs Based on Green’s Functions and Fixed-Point Iterative Schemes

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Abstract

This article discusses a numerical iterative scheme for the solution of a class of nonlinear singular boundary value problems. It introduces a recent approach, based on Green’s functions and Picard’s and Mann’s fixed-point iterations procedures, to tackle such problems. The convergence analysis of the proposed method is presented to verify its efficiency. A number of examples are given to demonstrate the applicability of the method. The numerical experiments show that this approach is better than many other existing techniques and that it is reliable, accurate and less time consuming.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE

    R. Assadi, S. A. Khuri & A. Sayfy

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  1. R. Assadi
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  2. S. A. Khuri
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  3. A. Sayfy
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Correspondence to S. A. Khuri.

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Assadi, R., Khuri, S.A. & Sayfy, A. Numerical Solution of Nonlinear Second Order Singular BVPs Based on Green’s Functions and Fixed-Point Iterative Schemes. Int. J. Appl. Comput. Math 4, 134 (2018). https://doi.org/10.1007/s40819-018-0569-8

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  • DOI: https://doi.org/10.1007/s40819-018-0569-8

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