Implementation of Aerodynamic Computations with Mathematica

Ganzha, Victor; Vorozhtsov, Evgenii V.

doi:10.1007/978-3-642-60218-4_8

Cited by 1 publication

(2 citation statements)

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“…Examples of the numerical solutions of some relatively simple one-, two-, and three-dimensional problems of continuum mechanics were presented in [3], which may be computed with acceptable CPU time expenses within the framework of Mathematica at a fairly moderate total number of spatial computing mesh nodes. An attempt to apply Mathematica for the numerical solution of two-dimensional problems of gas dynamics on curvilinear spatial computing meshes was implemented successfully in [4]. But it turned out that the developed Mathematica code had a computational speed, which was many times smaller than the speed of the corresponding Fortran code.…”

Section: Let Us Now Consider the Followingmentioning

confidence: 99%

“…The developers of the considered system recommended the use of the built-in function Compile[…] to accelerate the numerical computations in Mathematica. However, its application reduced the CPU time needed for solving the two-dimensional problems of gas dynamics only by the factor of 5/3 = 1.67 [4] rather than by the factor of 20, as it was declared in [1].…”

Section: Let Us Now Consider the Followingmentioning

confidence: 99%

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On Some Unsolved Problems of Mathematica

Vorozhtsov

2012

Eng. Technol. Appl. Sci. Res.

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In this paper, some unsolved problems of the Mathematica software package are documented. At first, it is shown, using a number of examples, that the processing (simplification) of rational-fractional expressions involving powers in the general form, has been implemented in Maple more carefully than in Mathematica. Then, an error in Mathematica is demonstrated, leading to incorrect results at a change of a function’s body. For each example of symbolic or symbolic-numeric computations, alternate routes for solving the emerged problem are proposed (where possible). An added problem, related to Mathematica’s computing speed is documented, employing examples related to two-dimensional gas dynamics problems. It is shown that Mathematica computes rather slowly (about one thousand times slower) compared to a Fortran code.

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Section: Let Us Now Consider the Followingmentioning

confidence: 99%

Section: Let Us Now Consider the Followingmentioning

confidence: 99%