On a Span Classsearchtermclassspan of High Resolution Total Variation
On a Span Classsearchtermclassspan of High Resolution Total Variation
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Scheme should be second order accurate almost everywhere. The details of the construction of such a g are given in the next section.
We would like to point out that the resulting second order accurate scheme has to be genuinely nonlinear, i. E. Nonlinear even in the constant coefficient case, since linear second order accurate TVD schemes do not exist (see [5]).
-26- 4, Second Order Accurate TVD Schanes In this section we convert the first order accurate TVD schemes of Corollary 3. A into secon...d order accurate ones by using a technique developed in [ 5] .
The basic idea is to use the first order accurate scheme with an appropriately modified flux f + _ g, i. E.
A ^^j+l/2 = 2 ^^j"^ ^j+l^ +2" ^®J^J+1^" 2 ^^''j+1/2 + ^j+l/2> ^j+1/2^ ^^'l^) where "^^4-1/2 = ^j+1/28 / ^j+1/2 ^ » i^. Lh) thus preserving the TVD property of the scheme.
The construction of g to be used in (4. 1) is done in two steps: First we use truncation error analysis to find the Taylor expansion of g for which (3. 5) with (4.
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To quickly assess the difficulty of the text, read a short excerpt:
Scheme should be second order accurate almost everywhere. The details of the construction of such a g are given in the next section.
We would like to point out that the resulting second order accurate scheme has to be genuinely nonlinear, i. E. Nonlinear even in the constant coefficient case, since linear second order accurate TVD schemes do not exist (see [5]).
-26- 4, Second Order Accurate TVD Schanes In this section we convert the first order accurate TVD schemes of Corollary 3. A into secon...d order accurate ones by using a technique developed in [ 5] .
The basic idea is to use the first order accurate scheme with an appropriately modified flux f + _ g, i. E.
A ^^j+l/2 = 2 ^^j"^ ^j+l^ +2" ^®J^J+1^" 2 ^^''j+1/2 + ^j+l/2> ^j+1/2^ ^^'l^) where "^^4-1/2 = ^j+1/28 / ^j+1/2 ^ » i^. Lh) thus preserving the TVD property of the scheme.
The construction of g to be used in (4. 1) is done in two steps: First we use truncation error analysis to find the Taylor expansion of g for which (3. 5) with (4.
What to read after On a Span Classsearchtermclassspan of High Resolution Total Variation?
You can find similar books in the "Read Also" column, or choose other free books by A Harten to read onlineMoreLess
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