# Accession Number:

## ADA011106

# Title:

## Marching Algorithms for Elliptic Boundary Value Problems II: The Non-Constant Coefficient Case.

# Descriptive Note:

## Technical rept. Sep 74-May 75,

# Corporate Author:

## HARVARD UNIV CAMBRIDGE MASS AIKEN COMPUTATION LAB

# Personal Author(s):

# Report Date:

## 1975-05-28

# Pagination or Media Count:

## 66.0

# Abstract:

The marching and generalized marching algorithms of Part I are extended to non-constant coefficient problems in which the elliptic operator is separable, once a suitable set of polynomials, which play a role analogous to the Chebyshev polynomials in the constant coefficient case, has been determined. These methods require On sup 2 and 0n sup 2 log nk operations, respectively, to solve a problem on an n x n grid, and have numerical stability characteristics similar to their constant coefficient counterparts. Problems in which the elliptic operator is not separable are treated using a DYakanov-Gunn iteration in which a sequence of separable problems is solved. The rate of convergence of this iteration is shown to be essentially independent of n.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics