Statistical analysis of error for fourth-order ordinary differential equation solvers

Bo He and Clyde Martin

Journal of Applied Statistics, 2009, vol. 36, issue 8, 835-852

Abstract: We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams-Bashforth method and a new method that randomly switches between the Milne and Adams-Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.

Keywords: differential equations; numerical error; switching (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1080/02664760802510034

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