Marching Algorithms for Elliptic Boundary Value Problems. I. The Constant Coefficient Case.
Technical rept. Sep 74-Apr 74,
HARVARD UNIV CAMBRIDGE MASS AIKEN COMPUTATION LAB
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Several new fast direct methods for solving constant coefficient elliptic boundary value problems are presented. The methods make extensive use of the algebraic properties of the modified Chebyshev polynomials S sub nx and C sub nx, which allow us to obtain operation counts of On squared or On squared logbase 2 for solving problems on an nXn grid. The algorithms are shown to be numerically stable by giving a Wilkinson-style error analysis. Previously studied fast direct methods, and shooting and multiple shooting techniques are related to the algorithms.
- Theoretical Mathematics