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{\large Hyoseop Lee \\
{\bf Higher-order schemes for the Laplace transformation method for parabolic problems}}

Mathematics Department \\ University of Wyoming \\ Laramie \\ Wyoming 82071-3036 \\ USA
\\
{\tt hyoseop.lee@gmail.com}\\
Craig. C. Douglas\\
Imbunm Kim\\
Dongwoo Sheen\end{center}

In the effective and efficient numerical approximation of parabolic
problems, there are three primary issues: the discretization in the time
variable, the discretization in the spatial variable, and the linear
solver used at each time step. In this work, we propose to solve linear
parabolic problems using three stage noble algorithms. The time
discretization is approximated using the Laplace transformation method,
which is both parallel and has extremely high order convergence. Higher
order compact schemes of order four and six are applied in the the
spatial discretization. Finally, the discretized linear algebraic systems
are solved using MADPACK, which is a highly efficient implementation of
various multigrid methods in an abstract problem setting. Numerical
results confirm the efficiency of the proposed method and show an ideal
parallel speed up on a traditional Linux computing cluster.


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