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Simple numerical methods of second- and third-order convergence for solving a fully third-order nonlinear boundary value problem

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Abstract

In this paper, we consider a fully third-order nonlinear boundary value problem that is of great interest of many researchers. First, we establish the existence and uniqueness of solution. Next, we propose simple iterative methods on both continuous and discrete levels. We prove that the discrete methods are of second-order and third-order of accuracy due to the use of appropriate formulas for numerical integration and obtain estimate for total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the iterative methods.

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Funding

The second author, Dang Quang Long, was supported by Institute of Information Technology, VAST under the project CS 20.01.

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Authors and Affiliations

  1. Centre for Informatics and Computing, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Quang A Dang

  2. Institute of Information Technology, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Quang Long Dang

  3. Lac Hong University, 10 Huynh Van Nghe, Bien Hoa, Dong Nai, Vietnam

    Quang A Dang

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  1. Quang A Dang
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  2. Quang Long Dang
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Correspondence to Quang A Dang.

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Dang, Q.A., Dang, Q.L. Simple numerical methods of second- and third-order convergence for solving a fully third-order nonlinear boundary value problem. Numer Algor 87, 1479–1499 (2021). https://doi.org/10.1007/s11075-020-01016-2

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  • DOI: https://doi.org/10.1007/s11075-020-01016-2

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