A NOTE ON THE APPROXIMATION OF PDES
WITH UNBOUNDED COEFFICIENTS - THE SPECIAL
F.F. Gonçalves1, M.R. Grossinho2, E. Morais3 1 CEMAPRE-REM and ISEG, Universidade de Lisboa
Rua do Quelhas 6, 1200-781 Lisbon, PORTUGAL
Also with Universidade Europeia
Estrada da Correia 53, 1500-210 Lisbon, PORTUGAL 2 CEMAPRE-REM and ISEG, Universidade de Lisboa
Rua do Quelhas 6, 1200-781 Lisbon, PORTUGAL 3 CMAT, Universidade do Minho
Campus de Gualtar, 4710-057 Braga, PORTUGAL
We consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients, where equation's free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [#!goncalves13!#], we consider a suitable variational framework and approximate the PDE problem's generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [#!goncalves13!#] for the more general multidimensional case.
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