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A symmetry group of this system is a local transformation G acting on M ⊂ X × U. which transforms solutions of the system to other solutions.
The transformed solutions are inverted numerically, using a numerical inversion technique to invert the Fourier transform.
The transformed solutions are obtained using the Fourier transform on the space variable.
For further analysis, statistical temporal moments are derived from the Laplace transformed solutions.
The system of governing equations is solved with the generalized Crank Nicholson method of central finite differences and approximate methods based on averaging certain process parameters, which use simple Laplace transform solutions for particular cases.
For these cases, high-resolution numerical integrations of the spectral transform model are used to provide reference solutions against which alternative numerical schemes and lower resolution spectral transform solutions can be evaluated.
In Section 2, we derive the Lie point symmetries of the DSWS using Lie group analysis and find the transformed solutions.
From a transform solution, approximations are derived and analysed for several configurations.
First, an exact transform solution for the auxiliary problem of multiple-zone (integer n > 1) surface tractions is obtained.
Assuming the disturbances to be harmonically time dependent, the transformed solution is obtained in the frequency domain.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com