Linear multistep methods with mildly varying coefficients

Lambert, J. D.

doi:10.1090/S0025-5718-1970-0280010-7

Linear multistep methods with mildly varying coefficients
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by J. D. Lambert PDF

Math. Comp. 24 (1970), 81-93 Request permission

Abstract:

Consideration of a common assumption in the theory of weak stability of linear multistep methods for ordinary differential equations leads to the study of a class of linear multistep methods with mildly varying coefficients. It is well known that, in the case of constant-coefficient methods, optimal stable methods suffer from weak instability. Corresponding methods of the new class, of step-number $2$ and $4$, which do not suffer from weak instability are derived.

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