TY - JOUR
T1 - The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 556
EP - 570
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.1111nm
UR - https://global-sci.org/intro/article_detail/nmtma/5918.html
KW - Partial integro-differential equation, weakly singular kernel, spectral collocation methods, $z$-transform, convolution quadrature.
AB - <p style="text-align: justify;">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.</p>