Type-insensitive ODE codes based on implicit 𝐴-stable formulas

Shampine, L. F.

doi:10.1090/S0025-5718-81-99841-0

Type-insensitive ODE codes based on implicit $A$-stable formulas
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Math. Comp. 36 (1981), 499-510 Request permission

Abstract:

A special concept of stiffness is appropriate for implicit A -stable formulas. It is possible to recognize this kind of stiffness economically and reliably using information readily available during the integration of an ODE. Using this development, a variety of effective ODE solvers could be made insensitive to the type of problem, i.e. the code would automatically recognize and alter automatically its algorithm at any step depending on whether the problem is stiff there.

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