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Sixth Order Numerical Method for Solving Second Order Nonlinear Boundary Value Problem

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Advances in Information and Communication Technology (ICTA 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 847))

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Abstract

In this paper we propose a numerical method of sixth order of accuracy for solving the Dirichlet problem for second order nonlinear differential equation. It is based on the use of sixth order difference schemes for second order linear boundary value problems and approximation of the first derivative by difference formulas with sixth order of accuracy at each iteration of a constructed iterative method on continuous level. The total error of the numerical solution is obtained. Many examples confirmed the accuracy of sixth order of the method and its advantages over some other methods.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.01–2021.03.

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Authors and Affiliations

  1. Center for Informatics and Computing, VAST, Hanoi, Vietnam

    Dang Quang A

  2. Thái Nguyên University of Information and Communication Technology, Thái Nguyên, Vietnam

    Truong Ha Hai

Authors
  1. Dang Quang A
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  2. Truong Ha Hai
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Corresponding author

Correspondence to Dang Quang A .

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Editors and Affiliations

  1. Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam

    Phung Trung Nghia

  2. Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam

    Vu Duc Thai

  3. VNU University of Engineering and Technology, Vietnam National University, Ha Noi, Vietnam

    Nguyen Thanh Thuy

  4. Information Technology Institute, Vietnam National University, Ha Noi, Vietnam

    Le Hoang Son

  5. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Quang A, D., Ha Hai, T. (2023). Sixth Order Numerical Method for Solving Second Order Nonlinear Boundary Value Problem. In: Nghia, P.T., Thai, V.D., Thuy, N.T., Son, L.H., Huynh, VN. (eds) Advances in Information and Communication Technology. ICTA 2023. Lecture Notes in Networks and Systems, vol 847. Springer, Cham. https://doi.org/10.1007/978-3-031-49529-8_33

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