A class of -stable advanced multistep methods

Authors:
Jack Williams and Frank de Hoog

Journal:
Math. Comp. **28** (1974), 163-177

MSC:
Primary 65L05

MathSciNet review:
0356519

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Abstract: A class of *A*-stable advanced multistep methods is derived for the numerical solution of initial value problems in ordinary differential equations. The methods, of all orders of accuracy up to ten, only require values of *y'* and are self starting. Results for the asymptotic behaviour of the discretization error and for estimating local truncation error are also obtained. The practical implementation of the fourth order method is described and the method applied to some stiff equations. Numerical comparisons are made with Gear's method.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1974-0356519-8

Keywords:
*A*-stable,
advanced multistep methods,
stiff systems

Article copyright:
© Copyright 1974
American Mathematical Society