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Two numerical limits of the scheme are obtained.

For the optimal design, the controller parameters of the proposed scheme are obtained with potential meta-heuristic technique named as cuckoo search algorithm (CSA).

Furthermore, the coefficient matrices entering the solution scheme are obtained by assembling the separate contribution of each branch, thus avoiding the ad hoc node numbering and branch orientation required by alternative implementations.

The stability estimates for the solution of this difference scheme are obtained.

The output signals after IFFT at the transmitter of this scheme are obtained from (9).

The grid spacings of difference scheme are obtained by analyzing numerical stability and convergence based on the maximal principle.

Finally, the optimized scheme was obtained.

A simple scheme is obtained, which can be easily implemented.

The compression scheme is obtained by using a custom designed hierarchical wavelet basis construction.

The VCA values of each experimental scheme were obtained through tamping test and vibrating compaction experiments.

By the Galerkin finite element method and backward difference method, a fully discrete scheme is obtained.