کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
523036 867902 2006 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences
چکیده انگلیسی

Finite differences approximate the mth derivative of a function u(x  ) by a series ∑j=-NNdj(m)u(xj), where the xj are the grid points. The closely-related discrete singular convolution (DSC) and Lagrange-distributed approximating function (LDAF) methods, treated here as a single algorithm, approximate derivatives in the same way as finite differences but with different numerical weights that depend upon a free parameter a. By means of Fourier analysis and error theorems, we show that the DSC is worse than the standard finite differences in differentiating exp(ikx) for all k when a ⩾ aFD where aFD≡1/N+1 with N as the stencil width is the value of the DSC parameter that makes its weights most closely resemble those of finite differences. For a < aFD, the DSC errors are less than finite differences for k near the aliasing limit, but much, much worse for smaller k. Except for the very unusual case of low-pass filtered functions, that is, functions with negligible amplitude in small wavenumbers k, the DSC/LDAF is less accurate than finite differences for all stencil widths N. So-called “spectrally-weighted” or “frequency-optimized” differences are superior for this special case. Consequently, DSC/LDAF methods are never the best way to approximate derivatives on a stencil of a given width.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 214, Issue 2, 20 May 2006, Pages 538–549
نویسندگان
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