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

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Chebyshev Polynomials
  • Coefficients
  • Error Analysis
  • Errors
  • Mathematics
  • Polynomials

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.