List Of Tables

List of Tables

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 $5(4)$ Dormand–Prince method.

Table 6:
Comparison, for the $D10−5$ 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, $D1 −2$ , (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.