Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/14104
Title: The regularized Whittaker-Kotel'nikov-Shannon sampling theorem and its application to the numerical solutions of partial differential equations
Authors: QIAN LIWEN
Keywords: Sampling theorem, regularization operator, error estimation, Gaussian, partial differential equation, numerical analysis
Issue Date: 8-Jul-2004
Source: QIAN LIWEN (2004-07-08). The regularized Whittaker-Kotel'nikov-Shannon sampling theorem and its application to the numerical solutions of partial differential equations. ScholarBank@NUS Repository.
Abstract: The Whittaker-Kotel'nikov-Shannon (WKS) sampling theorem has wide application in science and engineering. There exists an extensive literature addressing the problem of identifying specific regulators to accelerate the convergence of the truncated sampling series. This thesis develops a general analysis of regularization operators, with an emphasis on their ability to effectively approximate band-limited functions. In particular, our results explain why the Gaussian regularized sampling series works to a high degree of accuracy. Moreover, our analysis covers the multidimensional case and we also report on extensive numerical simulation with the use of these techniques for the numerical solution of various partial differential equations, including Burgers' equation, KdV equation, sine-Gorden equation and Schr\"odinger equation. In another direction we discuss the optimal estimation of band-limited functions from their sampled values. Finally, we give analysis of a collocation method using the regularized WKS sampling theorem for the 2D Poisson equation on a square.
URI: http://scholarbank.nus.edu.sg/handle/10635/14104
Appears in Collections:Ph.D Theses (Open)

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