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

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

Mathematical Problems in Engineering, 2021, vol. 2021, 1-27

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9917271

DOI: 10.1155/2021/9917271

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