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


Reference:

Spence, E. A. and Fokas, A. S., 2010. A new transform method II: the global relation and boundary-value problems in polar coordinates. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 466 (2120), pp. 2283-2307.

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    Official URL:

    http://dx.doi.org/10.1098/rspa.2009.0513

    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.

    Details

    Item Type Articles
    CreatorsSpence, E. A.and Fokas, A. S.
    DOI10.1098/rspa.2009.0513
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher Statementddfspaper2final.pdf: The definitive version is available from: http://dx.doi.org/10.1098/rspa.2009.0513
    RefereedYes
    StatusPublished
    ID Code27245

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