A Search for Better Linear Multistep Methods for Stiff Problems
ILLINOIS UNIV AT URBANA DEPT OF COMPUTER SCIENCE
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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.
- Numerical Mathematics