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Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation

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Abstract

In this paper, we consider a boundary value problem (BVP) for a fourth-order nonlinear integro-differential equation. By reducing the problem to an operator equation, we establish the existence and uniqueness of the solution and construct a numerical method for solving it. We prove that the method is of second-order accuracy and obtain an estimate for the total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the numerical method.

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Funding

This work is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant number 102.01-2021.03.

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Authors and Affiliations

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

    Dang Quang Long

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

    Dang Quang A

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

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Long, D.Q., A, D.Q. Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation. Numer Algor 90, 563–576 (2022). https://doi.org/10.1007/s11075-021-01198-3

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  • DOI: https://doi.org/10.1007/s11075-021-01198-3

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