_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/
\n_\/
\n_\/ \u6d41\u4f53\u529b\u5b66\u30bb\u30df\u30ca\u30fc \uff12\uff10\uff10\uff14 No. \uff14
\n_\/
\n_\/ \u65e5 \u6642 : \uff10\uff14\u5e74 \uff16\u6708 \uff11\uff14\u65e5 (\u6708) \uff11\uff15\uff1a\uff10\uff10\u301c\uff11\uff16\uff1a\uff13\uff10
\n_\/
\n_\/ \u5834 \u6240 : \u4eac\u5927\u6570\u7406\u7814 \uff10\uff10\uff19\u53f7\u5ba4
\n_\/
\n_\/ \u8b1b \u5e2b : Bernie Shizgal \u6c0f \uff08Department of Chemistry and
\n_\/ Institute of Applied Mathematics
\n_\/ University of British Columbia, Vancouver, CANADA\uff09
\n_\/
\n_\/ \u984c \u76ee : Spectral Methods and the Resolution of the Gibbs Phenomenon
\n_\/
\n_\/ \u5185 \u5bb9 :
\n_\/ Spectral methods involve the expansion of the solution of some partial
\n_\/ differential equation or integral equation in a set of basis functions.
\n_\/ The usual basis functions chosen are the Fourier functions or Chebyshev
\n_\/ polynomials. Recent work on the use of nonclassical basis functions will
\n_\/ be briefly dicussed. It is well known that the expansion of an analytic
\n_\/ nonperiodic function on a finite interval in a Fourier series leads to
\n_\/ spurious oscillations at the interval boundaries. This result is known
\n_\/ as the Gibbs phenomenon. The present talk describes a new method for the
\n_\/ resolution of the Gibbs phenomenon (Shizgal and Jung, J. Comput. Appl.
\n_\/ Math. 161 (2003) 41) which follows on the reconstruction method of
\n_\/ Gottlieb and coworkers (SIAM Rev. 39 (1997) 644) based on Gegenbauer
\n_\/ polynomials. We refer to their approach as the direct method and to the
\n_\/ new methodology as the inverse method. The direct method requires that
\n_\/ certain conditions are met concerning $\u00a5lambda$ in the weight function
\n_\/ $(1-x^2)^{\u00a5lambda-1\/2}$, the number of Fourier coefficients, $N$ and the
\n_\/ number of Gegenbauer polynomials, $m$. We show that the new inverse
\n_\/ method can give exact results for polynomials independent of $\u00a5lambda$
\n_\/ and with $m =3D N$. The paper presents several numerical examples
\n_\/ applied to a single domain or to subdomains of the main domain so as to
\n_\/ illustrate the superiority of the inverse method in comparison with the
\n_\/ direct method.
\n_\/
\n_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/
\n\u4e16\u8a71\u4eba\uff1a\u5927\u6728\u8c37 \u8015\u53f8(\u4eac\u5927\u6570\u7814)\u3001\u85e4 \u5b9a\u7fa9(\u4eac\u5927\u7406)\u3001\u677e\u672c \u525b(\u4eac\u5927\u7406)\u3001
\n\u5c71\u7530 \u9053\u592b(\u4eac\u5927\u6570\u7814)
\n\u30a2\u30c9\u30d0\u30a4\u30b6\u30fc\uff1a\u6cb3\u539f \u6e90\u592a(\u4eac\u5927\u5de5)\u3001\u5c0f\u68ee \u609f\uff08\u4eac\u5927\u5de5\uff09\u3001\u85e4\u5742\u535a\u4e00\uff08\u4eac\u5927\u60c5\u5831\u5b66\uff09\u3001
\n\u8239\u8d8a \u6e80\u660e\uff08\u4eac\u5927\u60c5\u5831\u5b66\uff09\u3001\u6c34\u5cf6 \u4e8c\u90ce(\u540c\u5fd7\u793e\u5927\u5de5)\u3001\u4f59\u7530 \u6210\u7537\uff08\u4eac\u5927\u7406\uff09
\n\u9023\u7d61\u5148\uff1aohkitani@kurims.kyoto-u.ac.jp
\n\u30e1\u30fc\u30eb\u30ea\u30b9\u30c8\u9023\u7d61\u5148\uff1a semi-adm@kyoryu.scphys.kyoto-u.ac.jp<\/p>\n","protected":false},"excerpt":{"rendered":"
_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/_\/ _\/ _\/ \u6d41\u4f53\u529b\u5b66\u30bb\u30df\u30ca\u30fc \uff12\uff10\uff10\uff14 No. \uff14 _\/ _\/ […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16,28],"tags":[],"class_list":["post-568","post","type-post","status-publish","format-standard","hentry","category-16","category-28"],"_links":{"self":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=568"}],"version-history":[{"count":0,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/568\/revisions"}],"wp:attachment":[{"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=568"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/kyoryu.scphys.kyoto-u.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}