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.