The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel
DOI:
https://doi.org/10.4208/nmtma.2013.1111nmKeywords:
Partial integro-differential equation, weakly singular kernel, spectral collocation methods, $z$-transform, convolution quadrature.Abstract
The $z$-transform is introduced to analyze a full discretization method for a partial integro-differential equation (PIDE) with a weakly singular kernel. In this method, spectral collocation is used for the spatial discretization, and, for the time stepping, the finite difference method combined with the convolution quadrature rule is considered. The global stability and convergence properties of complete discretization are derived and numerical experiments are reported.