Parabolic-elliptic correspondence of a three-level finite difference approximation to the heat equation
We consider three-level difference replacements of parabolic equations focussing on the heat equation in two- space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an ADI method. Using the well-known fact of the parabolic-elliptic correspondence, we shall deri...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
2003
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/6506/1/v26n1p8.pdf http://eprints.utm.my/id/eprint/6506/ |
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| Institution: | Universiti Teknologi Malaysia |
| Language: | English |
| Summary: | We consider three-level difference replacements of parabolic equations focussing on the heat equation in two- space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an ADI method. Using the well-known fact of the parabolic-elliptic correspondence, we shall derive a two-stage iterative procedure employing a fractional splitting strategy applied alternately at each intermediate time step. |
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