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ON THE SPACE DISCRETIZATION OF PDES WITH UNBOUNDED COEFFICIENTS ARISING IN FINANCIAL MATHEMATICS – THE CASE OF ONE SPATIAL DIMENSION

By F. F. Gonçalves, M. R. Grossinho and E. Morais

Abstract

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. 1. Introduction an

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.192.1685
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