Liao's absorbing boundary condition (ABC) is a classic ABC algorithm. It has the advantages of better absorption effect, easy programming and needless to split field. However its numerical stability is poor, especially for the higher-order ones, which greatly limits the scope of its application. To solve this problem, a weighting method for improving the stability of Liao's higher-order ABC is presented in this paper. This method is simple and effective, and it can be implemented easily compared with other improvement methods before. It improves the stability of Liao's higher-order ABC remarkably, and extends its application range.
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