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Multistep methods using higher derivatives and damping at infinity

Author: Rolf Jeltsch
Journal: Math. Comp. 31 (1977), 124-138
MSC: Primary 65L05
MathSciNet review: 0428716
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Abstract: Linear multistep methods using higher derivatives are discussed. The order of damping at infinity which measures the stability behavior of a k-step method for large h is introduced, A-stable methods with positive damping order are most suitable for stiff problems. A method for computing the damping order is given. Necessary and sufficient conditions for A-stability, A $ A(\alpha )$-stability and stiff stability are presented. A new A-stable two-step method of order 4 with damping order 1 is found and numerical results are given.

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Keywords: Ordinary differential equations, linear k-step methods using higher derivatives, Obrechkoff methods, Hermite methods, A-stable, order of damping at infinity, stiffly stable, strongly A-stable, L-stable
Article copyright: © Copyright 1977 American Mathematical Society