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Activity Number:
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369
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2008 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #300485 |
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Title:
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Numerical Error in ODEs
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Author(s):
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Clyde Martin*+ and Bo He
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Companies:
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Texas Tech University and Texas Tech University
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Address:
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Dept. of Mathematics and Statistics, Lubbock, TX, 79409,
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Keywords:
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differential equations ; numerical error ; switching
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Abstract:
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An autoregressive integrated moving average model (ARIMA) is developed to study the statistical behavior of the numerical error generated from three fourth-order ODE solvers: Milne's method, Adams-Bashforth method and a new method which randomly switches between Milne and Adams-Bashforth methods. With the error data based on four differential equations, we identify an ARIMA model for each data series. Results show that some of data series can be well described by ARIMA models but others can not. Based on the mathematical form of the numerical error, other statistical models should be investigated. Finally we assess the multivariate normality of the sample mean vectors which are generated by the switching method as an application of the multivariate central limit theorem. It is shown that the error for the switching method is well behaved.
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- Authors who are presenting talks have a * after their name.
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