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A quantitative probabilistic investigation into the accumulation of rounding errors in numerical ODE solution.

Mosbach, Sebastian and Turner, Amanda (2009) A quantitative probabilistic investigation into the accumulation of rounding errors in numerical ODE solution. Computers and Mathematics with Applications, 57 (7). pp. 1157-1167. ISSN 0898-1221

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    Abstract

    We examine numerical rounding errors of some deterministic solvers for systems of ordinary differential equations (ODEs) from a probabilistic viewpoint. We show that the accumulation of rounding errors results in a solution which is inherently random and we obtain the theoretical distribution of the trajectory as a function of time, the step size and the numerical precision of the computer. We consider, in particular, systems which amplify the effect of the rounding errors so that over long time periods the solutions exhibit divergent behaviour. By performing multiple repetitions with different values of the time step size, we observe numerically the random distributions predicted theoretically. We mainly focus on the explicit Euler and fourth order Runge–Kutta methods but also briefly consider more complex algorithms such as the implicit solvers VODE and RADAU5 in order to demonstrate that the observed effects are not specific to a particular method.

    Item Type: Article
    Journal or Publication Title: Computers and Mathematics with Applications
    Additional Information: The final, definitive version of this article has been published in the Journal, Computers and Mathematics with Applications 57 (7), 2009, © ELSEVIER.
    Uncontrolled Keywords: Rounding errors ; Markov jump processes ; Numerical ODE solution ; Limit theorem ; Saddle fixed point
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 26135
    Deposited By: Dr Amanda Turner
    Deposited On: 13 Mar 2009 14:47
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 13:12
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/26135

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