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논문 기본 정보
- 자료유형
- 학술대회자료
- 저자정보
- 발행연도
- 2005.5
- 수록면
- 15 - 16 (2page)
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초록· 키워드
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In the field of scalar hyperbolic equations, we take into consideration the idea of building numerical schemes using two grids: the first one to represent the solution and the second one to collocate the equation. This approach is based on the experience already gained in the approximation of boundary-value elliptic-type problems (see for instance [1]), as well as in the field of functional or integral-type equations (see [2]).
In order to show that the same approach can be used with success also for time-dependent problems, we study finite-difference approximations of first-order scalar hyperbolic equation in one space dimension. The representation grid is the usual uniform grid in the space-time plane. The discrete values of the solution are then assumed to be computed on a six-points stencil of such a representation grid. The approximating equations are deduced after collocation at a new point inside the stencil. It turns out that the possibility of varying the collocation point, gives a lot of freedom in the construction of the approximation method. First of all, this allows for the rediscovery of old methods and their critical analysis from a different point of view. Secondly, we have now the chance, by establishing a suitable relation between the representation and the collocation grids, to introduce new methods.
Since the position of the collocation point (two degrees of freedom) characterizes the approximation scheme, we can come out with a wide family ... 전체 초록 보기
In order to show that the same approach can be used with success also for time-dependent problems, we study finite-difference approximations of first-order scalar hyperbolic equation in one space dimension. The representation grid is the usual uniform grid in the space-time plane. The discrete values of the solution are then assumed to be computed on a six-points stencil of such a representation grid. The approximating equations are deduced after collocation at a new point inside the stencil. It turns out that the possibility of varying the collocation point, gives a lot of freedom in the construction of the approximation method. First of all, this allows for the rediscovery of old methods and their critical analysis from a different point of view. Secondly, we have now the chance, by establishing a suitable relation between the representation and the collocation grids, to introduce new methods.
Since the position of the collocation point (two degrees of freedom) characterizes the approximation scheme, we can come out with a wide family ... 전체 초록 보기
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UCI(KEPA) : I410-ECN-0101-2009-410-014677879