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Mathematics of Computation

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A class of $ A$-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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Keywords: A-stable, advanced multistep methods, stiff systems
Article copyright: © Copyright 1974 American Mathematical Society

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