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Mathematics of Computation

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Linear multistep methods with mildly varying coefficients

Author: J. D. Lambert
Journal: Math. Comp. 24 (1970), 81-93
MSC: Primary 65.61
MathSciNet review: 0280010
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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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Keywords: Linear multistep methods, weak stability, initial value problem, variable coefficient linear difference equations
Article copyright: © Copyright 1970 American Mathematical Society