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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 Solution of Robin-Dirichlet Problem for a Nonlinear Wave Equation with Memory Term

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  • @INPROCEEDINGS{10.1007/978-3-030-92942-8_15,
        author={Le Thi Mai Thanh and Tran Trinh Manh Dung and Nguyen Huu Nhan},
        title={Numerical Solution of Robin-Dirichlet Problem for a Nonlinear Wave Equation with Memory Term},
        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={Wave equation Faedo-Galerkin method Finite-difference method Robin-Dirichlet condition Memory term 35L05 35L15 35L20 35L55 35L70},
        doi={10.1007/978-3-030-92942-8_15}
    }
    
  • Le Thi Mai Thanh
    Tran Trinh Manh Dung
    Nguyen Huu Nhan
    Year: 2022
    Numerical Solution of Robin-Dirichlet Problem for a Nonlinear Wave Equation with Memory Term
    ICTCC
    Springer
    DOI: 10.1007/978-3-030-92942-8_15
Le Thi Mai Thanh1, Tran Trinh Manh Dung2, Nguyen Huu Nhan1,*
  • 1: Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Street
  • 2: Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, 227 Nguyen Van Cu Street
*Contact email: nhnhan@ntt.edu.vn

Abstract

In this paper, we propose a numerical procedure to find the approximate solution of initial-boundary value problem for a nonlinear wave equation with memory term. First, the local existence and uniqueness is proved by the linear approximating method and the Faedo-Galerkin method. Next, a numerical scheme is constructed by the finite-difference method and the standard arguments of ordinary differential equation. Finally, an example is given to simulate the numerical results of the proposed algorithm.

Keywords
Wave equation Faedo-Galerkin method Finite-difference method Robin-Dirichlet condition Memory term 35L05 35L15 35L20 35L55 35L70
Published
2022-01-03
Appears in
SpringerLink
http://dx.doi.org/10.1007/978-3-030-92942-8_15
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