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Advisor(s)
Abstract(s)
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 [10], 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 [10] for the more general multidimensional case.
Description
Keywords
Cauchy Problem Parabolic PDEs Unbounded Coefficients Non-divergent Operators Weighted Sobolev Spaces Finite-difference Methods
Pedagogical Context
Citation
Gonçalves, F.F.; Maria do Rosário Grossinho and E. Morais .(2020). “A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case”. International Journal of Applied Mathematics, Vol. 33, No. 1: pp: 137-156 : (Search PDF in 2023)
Publisher
Academic Publications