A new transform method II: the global relation and boundary-value problems in polar coordinates

Euan A Spence, A S Fokas

Research output: Contribution to journalArticle

19 Citations (Scopus)
125 Downloads (Pure)

Abstract

A new method for solving boundary-value problems (BVPs) for linear and certain nonlinear PDEs was introduced by one of the authors in the late 1990s. For linear PDEs, this method constructs novel integral representations (IRs) that are formulated in the Fourier (transform) space. In a previous paper, a simplified way of obtaining these representations was presented. In the current paper, first, the second ingredient of the new method, namely the derivation of the so-called ‘global relation’ (GR)—an equation involving transforms of the boundary values—is presented. Then, using the GR as well as the IR derived in the previous paper, certain BVPs in polar coordinates are solved. These BVPs elucidate the fact that this method has substantial advantages over the classical transform method.
Original languageEnglish
Pages (from-to)2283-2307
Number of pages25
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume466
Issue number2120
DOIs
Publication statusPublished - 2010

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