Electronic Resource
New York, NY [u.a.]
:
Wiley-Blackwell
Numerical Methods for Partial Differential Equations
12 (1996), S. 147-159
ISSN:
0749-159X
Keywords:
Mathematics and Statistics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
Several methods are presented for solving separable elliptic partial differential equations over an irregular region B using alternating direction collocation on a rectangular grid over an embedding rectangle R. The methods are geometric predictor-corrector schemes. At each iterative step, the numerical solution is predicted on R via a full ADI sweep. The forcing term is then updated (corrected) on collocation points interior to B. By this means, the geometry of B and boundary conditions on ∂B are approximated implicitly using rectangular grids on R. The methods are O(h4) in the L2(R) norm and are boundary exact, in that the computed solution converges exactly to the given boundary conditions on ∂B for appropriate choices of a pair of acceleration parameters. A number of examples are presented. Proof of convergence is established elsewhere. © 1996 John Wiley & Sons, Inc.
Additional Material:
4 Ill.
Type of Medium:
Electronic Resource
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