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.

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