Multistep methods using higher derivatives and damping at infinity

Author:
Rolf Jeltsch

Journal:
Math. Comp. **31** (1977), 124-138

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0428716-7

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* -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

DOI:
https://doi.org/10.1090/S0025-5718-1977-0428716-7

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