Variable-step variable-order algorithm for the numerical solution of neutral functional differential equations

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The variable-step variable-order algorithm based on predictor-corrector methods for neutral functional differential equations is described. The algorithm is implemented in interpolation mode, i.e. we use fixed-step formulation of Adams-Bashford Adams-Moulton formulas while all back-values are computed by interpolation. The local discretization error is estimated by Milne's device. Although the assumptions under which this estimate is asymptotically correct are rather strong and not always expected to be satisfied in practice, the numerical experiments up to date indicate that this algorithm can be quite accurate and efficient.

Original languageEnglish (US)
Pages (from-to)317-329
Number of pages13
JournalApplied Numerical Mathematics
Volume3
Issue number4
DOIs
StatePublished - 1987
Externally publishedYes

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Neutral Functional Differential Equation
Differential equations
Numerical Solution
Interpolation
Interpolate
Predictor-corrector Methods
Discretization Error
Numerical Experiment
Formulation
Estimate
Experiments

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

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abstract = "The variable-step variable-order algorithm based on predictor-corrector methods for neutral functional differential equations is described. The algorithm is implemented in interpolation mode, i.e. we use fixed-step formulation of Adams-Bashford Adams-Moulton formulas while all back-values are computed by interpolation. The local discretization error is estimated by Milne's device. Although the assumptions under which this estimate is asymptotically correct are rather strong and not always expected to be satisfied in practice, the numerical experiments up to date indicate that this algorithm can be quite accurate and efficient.",
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AB - The variable-step variable-order algorithm based on predictor-corrector methods for neutral functional differential equations is described. The algorithm is implemented in interpolation mode, i.e. we use fixed-step formulation of Adams-Bashford Adams-Moulton formulas while all back-values are computed by interpolation. The local discretization error is estimated by Milne's device. Although the assumptions under which this estimate is asymptotically correct are rather strong and not always expected to be satisfied in practice, the numerical experiments up to date indicate that this algorithm can be quite accurate and efficient.

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