STABILITY AND CONVERGENCE OF VARIABLE ORDER MULTISTEP METHODS.

C. W. Gear, D. S. Watanabe

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

A method based on variable step Adams formulas is shown to be stable for any order changing scheme. A method based on the Nordsieck form of Adams formulas, however, is shown to be stable only if the step size and order are fixed for p steps following a change to an r-step formula, where p is r or r plus 1 depending on the algorithm used to interpolate the necessary higher derivatives. Finally, general methods based on consistent and strongly stable multistep and multivalue formulas are shown to be stable if the formula is fixed for a certain number of steps following each formula change and if step size changes are small. This number is independent of the differential equation and the step sizes.

Original languageEnglish (US)
Pages (from-to)1044-1058
Number of pages15
JournalSIAM Journal on Numerical Analysis
Volume11
Issue number5
StatePublished - Jan 1 1974

All Science Journal Classification (ASJC) codes

  • Numerical Analysis

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