Title: Inverse problems for DEs and PDEs using the collage theorem: a survey

Authors: Herb Kunze; Davide La Torre; Franklin Mendivil; Edward Vrscay

Addresses: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada ' Department of Economics, Management and Quantitative Methods, University of Milan, Via Conservatorio 7, 20122 Milano, Italy ' Department of Mathematics and Statistics, Acadia University, Wolfville, Nova Scota, B4P 2R6, Canada ' Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Abstract: In this paper, we present several methods based on the collage theorem and its extensions for solving inverse problems for initial value and boundary value problems. Several numerical examples show the quality of this approach and its stability. At the end we present an application to the Euler-Bernoulli beam equation with boundary measurements.

Keywords: inverse problems; collage theorem; initial value problems; boundary value problems; differential equations; PDEs; partial differential equations.

DOI: 10.1504/IJANS.2013.052752

International Journal of Applied Nonlinear Science, 2013 Vol.1 No.1, pp.30 - 51

Received: 22 Aug 2012
Accepted: 11 Sep 2012

Published online: 30 Jul 2014 *

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