On convergent rate of the attractor for a singularly perturbed wave equation

2018 ◽  
Vol 316 ◽  
pp. 370-380
Author(s):  
Xiaoming Fan
Keyword(s):  
Wave Equation ◽  
Singularly Perturbed ◽  
Convergent Rate

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

2021 ◽  
Vol 2021 ◽  
pp. 1-27
Author(s):  
Doan Thi Nhu Quynh ◽  
Bui Duc Nam ◽  
Le Thi Mai Thanh ◽  
Tran Trinh Manh Dung ◽  
Nguyen Huu Nhan
Keyword(s):  
Wave Equation ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
High Order ◽  
Recurrent Sequence ◽  
Viscoelastic Wave Equation ◽  
Proposed Model ◽  
Viscoelastic Wave ◽  
Convergent Rate ◽  
The Galerkin Method

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 N -order iterative scheme is established, and then the N -order convergent rate of the obtained sequence to the unique weak solution of the proposed model is also proved. Next, with N = 2 , 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.

scholarly journals Uniform exponential attractors for a singularly perturbed damped wave equation

2003 ◽  
Vol 10 (1-2) ◽  
pp. 211-238 ◽  
Author(s):  
Pierre Fabrie ◽  
Cedric Galusinski ◽  
A. Miranville ◽  
Sergey Zelik
Keyword(s):  
Wave Equation ◽  
Singularly Perturbed ◽  
Damped Wave Equation ◽  
Exponential Attractors
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