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Mathematics of Computation

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Type-insensitive ODE codes based on implicit $ A(\alpha )$-stable formulas

Author: L. F. Shampine
Journal: Math. Comp. 39 (1982), 109-123
MSC: Primary 65L05
MathSciNet review: 658216
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Abstract: Previous work on A-stable formulas is extended to $ A(\alpha )$-stable formulas, which are far more important in practice. Some important improvements in technique based on another interation method and an idea of Enright for the efficient handling of Jacobians are proposed. Implementation details and numerical examples are provided for a research-grade code.

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Keywords: ODE codes, stiffness, $ A(\alpha )$-stable
Article copyright: © Copyright 1982 American Mathematical Society