TY - JOUR
T1 - A High Order Parallel Method for Time Discretization of Parabolic Type Equations Based on Laplace Transformation and Quadrature
AU - Thomée , Vidar
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 85
EP - 96
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/922.html
KW - parabolic type, Laplace transform, parallel method and high order quadrature.
AB - <p style="text-align: justify;">We consider the discretization in time of a parabolic
equation, using a representation of the solution as an integral along a
smooth curve in the complex left half plane. The integral is then
evaluated to high accuracy by a quadrature rule. This reduces the
problem to a finite set of elliptic equations, which may be solved in
parallel. The procedure is combined with finite element discretization
in the spatial variables. The method is also applied to some parabolic
type evolution equations with memory.</p>