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

T. Lu, W. Cai & P. Zhang

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 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 = {T. Lu, W. Cai and P. Zhang}, 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 - T. Lu, W. Cai & P. Zhang 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 KW - Laplace KW - 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.
T. Lu, W. Cai & P. Zhang. (1970). 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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