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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Multistep methods using higher derivatives and damping at infinity
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by Rolf Jeltsch PDF
Math. Comp. 31 (1977), 124-138 Request permission

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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Math. Comp. 31 (1977), 124-138
  • MSC: Primary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1977-0428716-7
  • MathSciNet review: 0428716