Table 1:
The structure of a Butcher table. |

Table 2:
From left to right: The Euler method, second and third-order RK, third-order Heun. |

Table 3:
The standard fourth-order Runge–Kutta method. |

Table 4:
The structure of embedded methods. |

Table 5:
The Dormand–Prince method. |

Table 6:
Comparison, for the operator, of both the spectral radius and average boundary truncation error (ABTE) when minimizing the bandwidth or a combination of the spectral radius and ABTE. For comparison, the spectral radius and ABTE for the lowest-accuracy operator, , (which is unique) are 1.414 and 0.25, respectively. Note: the ABTE, as defined, is larger for this operator, but its convergence rate is faster. |

Living Rev. Relativity 15, (2012), 9
http://www.livingreviews.org/lrr-2012-9 |
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