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A finite element method, combined with Newton iteration scheme, is one of most efficient numerical methods.
A large-update interior point method (IPM) is one of the most efficient numerical methods for various optimization problems.
One can summarize that the proposed method gives the most efficient numerical results in respect of both conservation and periodicity.
Finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates.
In the setting of Hilbert spaces, one of the most efficient numerical techniques is the projection method and its variant forms; see [4, 6 15].
The L1-scheme has been extensively used in practice and currently it is one of the most efficient numerical methods for solving the time fractional differential equations due to its ease of implementation.
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Multigrid methods (MGs) [8, 9] have been shown to be one of the most efficient modern numerical strategies to solve the large linear systems arising from FE or FD discretizations of partial differential equations (PDEs), such as the Poisson equation [10 14], Helmholtz equation [15 17], convection diffusion equation [18 20].
For computing interactions between dark and bright solitons, we compare the efficiency and accuracy of the above numerical methods and different existing numerical methods for computing bright solitons of NLSE, and identify the most efficient and accurate numerical methods for computing dark and bright solitons as well as their interactions in NLSE.
These non-uniform grids are expensive to calculate and cannot be used with the most accurate or efficient numerical schemes.
Three-dimensional time-dependent computations in most cases require an efficient numerical formulation as well as code parallelization.
In general setups, one has to resort to suboptimal solutions, most of them based on efficient numerical integration methods [6].
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