Mathematics – Numerical Analysis
Scientific paper
2005-12-15
Computers and Mathematics with Applications, Vol 57, No. 7, April 2009, 1157-1167
Mathematics
Numerical Analysis
17 pages, 7 figures
Scientific paper
10.1016/j.camwa.2009.01.020
We examine numerical rounding errors of some deterministic solvers for systems of ordinary differential equations (ODEs). We show that the accumulation of rounding errors results in a solution that 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 RK4 methods but also briefly consider more complex algorithms such as the implicit solvers VODE and RADAU5.
Mosbach Sebastian
Turner Amanda G.
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