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Volume 2, Issue 1
A High Order Parallel Method for Time Discretization of Parabolic Type Equations Based on Laplace Transformation and Quadrature

Vidar Thomée

Int. J. Numer. Anal. Mod., 2 (2005), pp. 85-96.

Published online: 2005-02

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  • Abstract

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.

  • Keywords

parabolic type, Laplace transform, parallel method and high order quadrature.

  • AMS Subject Headings

65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-85, author = {Thomée , Vidar}, title = {A High Order Parallel Method for Time Discretization of Parabolic Type Equations Based on Laplace Transformation and Quadrature}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {1}, pages = {85--96}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/922.html} }
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 -

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.

Thomée , Vidar. (2005). A High Order Parallel Method for Time Discretization of Parabolic Type Equations Based on Laplace Transformation and Quadrature. International Journal of Numerical Analysis and Modeling. 2 (1). 85-96. doi:
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