{"id":2870,"date":"2023-04-20T13:35:36","date_gmt":"2023-04-20T11:35:36","guid":{"rendered":"https:\/\/imm.webs.upv.es\/?p=2870"},"modified":"2025-01-30T14:32:12","modified_gmt":"2025-01-30T13:32:12","slug":"talk-of-prof-arieh-iserles-an-overarching-framework-for-spectral-methods-and-dispersive-equations","status":"publish","type":"post","link":"https:\/\/imm.webs.upv.es\/es\/talk-of-prof-arieh-iserles-an-overarching-framework-for-spectral-methods-and-dispersive-equations\/","title":{"rendered":"Charla del Prof. Arieh Iserles: An overarching framework for spectral methods and dispersive equations"},"content":{"rendered":"\n

El pr\u00f3ximo martes, 25 d’abril, a las 12:30, en el I.U. de Matem\u00e1tica Multidisciplinar, el Prof. Arieh Iserles, Profesor Em\u00e9rito de An\u00e1lisis Num\u00e9rico de Ecuaciones Diferenciales a la Universidad de Cambridge har\u00e1 una charla sobre m\u00e9todos espectrales y ecuaciones dispersivas.<\/p>\n\n\n\n

La puedes seguir online en: https:\/\/teams.microsoft.com\/l\/meetup-join\/19%3aac3291a8974744de9ff32dbfa56c36c4%40thread.tacv2\/1681991092801?context=%7b%22Tid%22%3a%22be4655df-ac73-401f-a7ae-198c3b72d0c6%22%2c%22Oid%22%3a%22bfd5fc16-28c0-4ab1-b7c1-451c80a4affb%22%7d<\/a><\/p>\n\n\n\n

Autor:<\/h2>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n

Arieh Iserles
Emeritus Professor in Numerical Analysis of Differential Equations
Department of Applied Mathematics and Theoretical Physics
Centre for Mathematical Sciences
University of Cambridge
Academic Portfolio <\/a><\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

Abstract:<\/h2>\n\n\n\n


Every spectral method commences from an orthonormal system \u03a6=\u03c6\u2099 n \u2208 \u2124\u208a over an interval (a,b) and its major feature is the differentiation matrix<\/em> \ud835\udc9f such that <\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n


Once \ud835\udc9f is skew-Hermitian, exp(t\u00b7\ud835\udc9f) is unitary and the method is stable and preserves the L\u2082 norm.<\/p>\n\n\n\n

The nature of the interval (a,b) and the boundary conditions is critical: periodic boundary conditions in a compact interval are a no-brainer: we use a Fourier basis. This leaves out three important 
scenarios: the real line (\u2212\u221e,\u221e), the half-line (0,\u221e) and the interval (-1,1), the latter two with zero Dirichlet boundary conditions. In the case of the real line we show that the additional requirement that \ud835\udc9f is tridiagonal leads to a complete characterisation of all orthonormal and complete sets \u03a6 by means of a Fourier transform, the Favard theorem and the Plancherel theorem. The half-line and a compact interval require a completely different approach. We show that in each case there exists an orthonormal set which leads to a skew-symmetric matrix \ud835\udc9f which, although dense, lends itself to very fast algebraic computations, and a magical value of the parameter that results in much improved accuracy.<\/p>\n","protected":false},"excerpt":{"rendered":"

Next Tuesday, April 25th, at 12:30 in the I.U. de Matem\u00e1tica Multidisciplinar, Prof. Arieh Iserles, Emeritus Professor in Numerical Analysis of Differential Equations of University of Cambridge will present a talk about spectral methods and dispersive equations. Show more<\/a><\/p>\n","protected":false},"author":4,"featured_media":2871,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-2870","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-talks-seminars"],"translation":{"provider":"WPGlobus","version":"3.0.2","language":"es","enabled_languages":["en","ca","es"],"languages":{"en":{"title":true,"content":true,"excerpt":true},"ca":{"title":true,"content":true,"excerpt":false},"es":{"title":true,"content":true,"excerpt":false}}},"yoast_head":"\nCharla del Prof. Arieh Iserles: An overarching framework for spectral methods and dispersive equations - I. 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