Marching Algorithms for Elliptic Boundary Value Problems. I. The Constant Coefficient Case.
Abstract
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 n)(x) and (C sub n)(x), which allow us to obtain operation counts of O(n squared) or O(n squared) (log(base 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1975
- Accession Number
- ADA009954
Entities
People
- Donald J. Rose
- Randolph E. Bank
Organizations
- Harvard University