A class of 𝐴-stable advanced multistep methods

Williams, Jack; de Hoog, Frank

doi:10.1090/S0025-5718-1974-0356519-8

A class of $A$-stable advanced multistep methods
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Math. Comp. 28 (1974), 163-177 Request permission

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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