Higher-order schemes for the Laplace transformation method for parabolic problems

Douglas, C.; Kim, I.; Lee, H.; Sheen, D.

Higher-order schemes for the Laplace transformation method for parabolic problems

Type

Article

Authors

Douglas, C.
Kim, I.
Lee, H.
Sheen, D.

KAUST Grant Number

KUS-C1-016-04

Online Publication Date

2011-09-03

Print Publication Date

2011-01

Date

2011-09-03

Abstract

In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.

Citation

Douglas C, Kim I, Lee H, Sheen D (2011) Higher-order schemes for the Laplace transformation method for parabolic problems. Computing and Visualization in Science 14: 39–47. Available: http://dx.doi.org/10.1007/s00791-011-0156-6.

Acknowledgements

The research by Prof. Douglas is based on work supported in part byNSF grants CNS-1018072 and CNS-1018079 and Award No. KUS-C1-016-04, made by the King Abdullah University of Science and Tech-nology (KAUST). The research by Prof. Sheen was partially supportedby NRF-2008-C00043 and NRF-2009-0080533, 0450-20090014. Theresearch by H. Lee was partially supported by Seoul R & D ProgramWR080951.