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Nature of Computation and Communication. 7th EAI International Conference, ICTCC 2021, Virtual Event, October 28–29, 2021, Proceedings

Research Article

Numerical Results via High-Order Iterative Scheme to a Nonlinear Wave Equation with Source Containing Two Unknown Boundary Values

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  • @INPROCEEDINGS{10.1007/978-3-030-92942-8_17,
        author={Pham Nguyen Nhat Khanh and Le Thi Mai Thanh and Tran Trinh Manh Dung and Nguyen Huu Nhan},
        title={Numerical Results via High-Order Iterative Scheme to a Nonlinear Wave Equation with Source Containing Two Unknown Boundary Values},
        proceedings={Nature of Computation and Communication. 7th EAI International Conference, ICTCC 2021, Virtual Event, October 28--29, 2021, Proceedings},
        proceedings_a={ICTCC},
        year={2022},
        month={1},
        keywords={Nonlinear wave equation High-order iterative scheme 2-order iterative scheme Finite-difference scheme Numerical results 35L20 35L70 35Q72},
        doi={10.1007/978-3-030-92942-8_17}
    }
    
  • Pham Nguyen Nhat Khanh
    Le Thi Mai Thanh
    Tran Trinh Manh Dung
    Nguyen Huu Nhan
    Year: 2022
    Numerical Results via High-Order Iterative Scheme to a Nonlinear Wave Equation with Source Containing Two Unknown Boundary Values
    ICTCC
    Springer
    DOI: 10.1007/978-3-030-92942-8_17
Pham Nguyen Nhat Khanh1, Le Thi Mai Thanh1, Tran Trinh Manh Dung1, Nguyen Huu Nhan2,*
  • 1: Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, 227 Nguyen Van Cu Street
  • 2: Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Street
*Contact email: nhnhan@ntt.edu.vn

Abstract

In the present paper, we consider an initial-boundary value problem for nonlinear equation in which the source term contains two boundary values. First, the local existence and uniqueness of a weak solution to this problem is inferred directly from [12], in which a recurrent sequence via aN-order iterative scheme is established and then theN-order convergent rate of the sequence to the unique weak solution of the proposed model is also proved. As(N=2), the corresponding scheme called 2-order iterative scheme is considered, and a numerical algorithm to calculate approximate solutions via the 2-order iterative scheme is constructed by the finite-difference method. Finally, a numerical example is presented to evaluate the errors between the exact solution and the approximate solution. The numerical results show that the errors are decreasing as the fineness of meshes is increasing.

Keywords
Nonlinear wave equation High-order iterative scheme 2-order iterative scheme Finite-difference scheme Numerical results 35L20 35L70 35Q72
Published
2022-01-03
Appears in
SpringerLink
http://dx.doi.org/10.1007/978-3-030-92942-8_17
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