A fourth-order compact BVM scheme for the two-dimensional heat equations
Sun H.-W.1; Wang W.2
Source PublicationProceedings of the 2008 International Conference on Scientific Computing, CSC 2008
AbstractIn this paper we combine the boundary value methods (for discretizing the temporal variable) and finite difference compact scheme (for discretizing the spatial variables) to numerically solve the two-dimensional heat equations. We firstly employ a fourth-order compact scheme to discretize the spatial derivatives. Then a linear system of ordinary differential equation is obtained. Then we apply a fourth-order scheme of boundary value method to approach this system. Therefore, this scheme can achieve fourth-order accuracy for both temporal and spatial variables, and it is unconditionally stable due to the favorable stability property of the boundary value methods. Numerical results are presented to illustrate the accuracy and efficiency of this compact difference scheme, compared with the classical second-order Crank-Nicolson scheme.
KeywordBVMs Compact difference scheme Crank-Nicolson Heat equation Unconditional stability
URLView the original
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Document TypeConference paper
CollectionUniversity of Macau
Affiliation1.Universidade de Macau
2.Chinese University of Hong Kong
Recommended Citation
GB/T 7714
Sun H.-W.,Wang W.. A fourth-order compact BVM scheme for the two-dimensional heat equations[C],2008:310-314.
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