On the space discretization of pdes with unbounded coefficients arising in financial mathematics. a case of one spatial dimension

Fernando F. Gonçalves, Maria do Rosario Grossinho, Eva Morais

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    Abstract

    We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spatial dimension and unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, the problem's weak solution is approximated in space, with finite-difference methods. The rate of convergence is estimated. A numerical example is given in order to illustrate the theoretical results.

    Original languageEnglish
    Pages (from-to)35-46
    Number of pages12
    JournalComptes Rendus de L'Academie Bulgare des Sciences
    Volume63
    Issue number1
    Publication statusPublished - 2010

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