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High-Order Iterative Scheme for a Viscoelastic Wave Equation and Numerical Results

Author

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  • Doan Thi Nhu Quynh
  • Bui Duc Nam
  • Le Thi Mai Thanh
  • Tran Trinh Manh Dung
  • Nguyen Huu Nhan

Abstract

In this paper, we consider a Robin problem for a viscoelastic wave equation. First, by the high-order iterative method coupled with the Galerkin method, the existence of a recurrent sequence via an - order iterative scheme is established, and then the - order convergent rate of the obtained sequence to the unique weak solution of the proposed model is also proved. Next, with , a numerical algorithm given by the finite-difference method is constructed to approximate the solution via the 2-order iterative scheme. Moreover, the same algorithm for the single-iterative scheme generated by the 2-order iterative scheme is also considered. Finally, comparison with errors of the numerical solutions obtained by the single-iterative scheme and the 2-order iterative scheme shows that the convergent rate of the 2-order iterative scheme is faster than that of the single-iterative scheme.

Suggested Citation

  • Doan Thi Nhu Quynh & Bui Duc Nam & Le Thi Mai Thanh & Tran Trinh Manh Dung & Nguyen Huu Nhan, 2021. "High-Order Iterative Scheme for a Viscoelastic Wave Equation and Numerical Results," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-27, June.
    • Handle: RePEc:hin:jnlmpe:9917271
    DOI: 10.1155/2021/9917271
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