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.
Fernando F. Gonçalves. Maria Rosário Grossinho. "Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance." Abstr. Appl. Anal. 2014 (SI27) 1 - 11, 2014. https://doi.org/10.1155/2014/801059