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Abstract and Applied Analysis
Volume 2014, Article ID 801059, 11 pages
Research Article

Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance

1CEMAPRE & Departmento de Matemática, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal
2Universidade Europeia, Estrada da Correia 53, 1500-210 Lisboa, Portugal

Received 26 July 2013; Accepted 5 January 2014; Published 6 March 2014

Academic Editor: István Györi

Copyright © 2014 Fernando F. Gonçalves and Maria Rosário Grossinho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the spatial discretisation of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients. The equation free term and the initial data are also allowed to grow. Under a nondegeneracy assumption, we consider the PDE solvability in the framework of the variational approach and approximate in space the PDE problem's generalised solution, with the use of finite-difference methods. The rate of convergence is estimated.