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Numerical results demonstrate that the scheme is efficient and accurate.
Numerical examples demonstrate that the scheme is fast and highly accurate.
Numerical simulation and security analysis demonstrate that the scheme is practical in image encryption.
In particular, the power-switching scheme is validated to demonstrate that the scheme proposed in this paper can solve these key problems for international applications.
Numerical examples are provided to demonstrate that the scheme can be successfully applied in complex problems, including cases of nonlinear diffusion.
Numerical experiments demonstrate that the scheme is capable of solving Helmholtz-type equations on a domain of size 20×20×20 wavelengths to three correct digits on a modest personal workstation, with N≈2⋅106.
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Numerical experiments demonstrate that the schemes are accurate and efficient.
Numerical experiments demonstrate that the schemes possess the AP property for general initial data, with numerical accuracy uniformly in the Knudsen number.
Numerical experiments demonstrate that the schemes produce accurate numerical solutions with the same stability restrictions as in the purely hyperbolic case.
It is demonstrated, that the scheme offers high accuracy and robustness while keeping the computational cost low.
(c) The record in this case demonstrates that the scheme Liggett alleged, when judged against the market's realities, does not provide an adequate basis for a finding of liability.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com