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The new scheme has been rigorously tested against a simple theoretical solution to Darcy's law as well as a more complicated example solved by numerical software packages with anisotropic flow capabilities.
Meanwhile, in order to demonstrate the effectiveness of the proposed method, the results of numerical example solved by PSO-SA are compared with a branch-and-bound method and other heuristic algorithms.
Numerical example solved by using Matlab software.
We coded the proposed GA solution method by MATLAB 2010 and applied the program to the same numerical example solved by the LINGO Software using the same desktop PC mentioned above and discussed in "Solving the model with LINGO software".
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Finally, some significant examples solved by this prototype are presented.
A number of examples solved by using triangular and bilinear elements are presented to show that the method can convect contact discontinuities without error.
It was shown by way of many examples––solved by numerous mathematical, as well as other heuristic approaches in the literature that the purposed methodology is quite efficient and capable of finding lighter and reasonable structural designs than that reported in the literature.
This example is solved by the GMCLP model and covered demand is 153.4.
A simple but general numerical example is solved by approximate analytical methods, by the Taylor series procedure and by a commercial probabilistic computer program (PROBAN).
This example is solved by the LINGO 8.0 software for the CMCLAP and the CGMCLAP models.
To validate the proposed ODE based approach, the same example is solved by using DE.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com