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Total variation diminishing : ウィキペディア英語版
Total variation diminishing
In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this method is in computational fluid dynamics. The concept of TVD was introduced by Ami Harten.
==Model equation==
In systems described by partial differential equations, such as the following hyperbolic advection equation,
:\frac + a\frac = 0,
the total variation (TV) is given by,
:TV = \int \left| \frac \right| dx ,
and the total variation for the discrete case is,
:TV = \sum_j \left| u_ - u_j \right| .
A numerical method is said to be total variation diminishing (TVD) if,
:TV \left( u^\right) \leq TV \left( u^\right) .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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