Accession Number:

ADA374153

Title:

A Search for Better Linear Multistep Methods for Stiff Problems

Descriptive Note:

Master's thesis

Corporate Author:

ILLINOIS UNIV AT URBANA DEPT OF COMPUTER SCIENCE

Personal Author(s):

Report Date:

1977-12-01

Pagination or Media Count:

112.0

Abstract:

For arbitrary k - 1 and alpha epsilon O,pi2, Aalpha-stable k-th order k-step formulas exist, so that in an ODE solver, a can be an extra parameter used to identify among a family of methods of order k the Aalpha-stable method that should be used for the particular problem. Two measures for assessing the accuracy of k-th order k-step formulas are proposed. The problem of finding the upper bound on the angle of absolute stability for the k-th order k-step formulas having the same accuracy with respect to one of the measures is considered. Analytical results are obtained for k 1, 2, 3 whereas a numerical search is used for the cases when k 4, 5, 6, 7.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE