A new transform method I: domain-dependent fundamental solutions and integral representations


Spence, E. A. and Fokas, A. S., 2010. A new transform method I: domain-dependent fundamental solutions and integral representations. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 466 (2120), pp. 2259-2281.

Related documents:

PDF (ddfspaper1final.pdf) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (252kB) | Preview

    Official URL:

    Related URLs:


    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 this paper, we present a simplified way of obtaining these representations for elliptic PDEs; namely, we introduce an algorithm for constructing particular, domain-dependent, IRs of the associated fundamental solutions, which are then substituted into Green's IRs. Furthermore, we extend this new method from BVPs in polygons to BVPs in polar coordinates. In the sequel to this paper, these results are used to solve particular BVPs, which elucidate the fact that this method has substantial advantages over the classical transform method.


    Item Type Articles
    CreatorsSpence, E. A.and Fokas, A. S.
    Related URLs
    URLURL Type
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher Statementddfspaper1final.pdf: The definitive version is available from:
    ID Code27071


    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...