The selection is based on a stability test that detects growing numerical noise and deems a method of order p stable if there is no method of lower order that delivers the same solution accuracy for a larger stepsize.
Suppose that a symmetric one-step method Φ τ is of even order p. Then a method of order p + 2 can be constructed by composition (see e.g. [5, p. 43]).
In addition, we observe superior performance for high precision requirements when the iterated fourth order method is compared to the (classic) triple jump scheme (which is a method of order three).
In the present paper, we follow the idea of Jain et al. [5, 28] but use non-polynomial tension spline approximation to develop an method of order four for the solution of a wave equation in polar co-ordinates with a significant first-order derivative term.
A synthetic method of ordering hydrophilic gold nanoparticles into a close-packed two-dimensional array at a hexane water interface and subsequent transferring of such structure onto a solid substrate is described.
In large teams where ranking is complex because many have contributed relatively evenly, a mixed method of ordering may be applied: the first few authors are listed according to the importance of contribution in descending order, while others are named in alphabetical order.
Dowding replied that the speed and altitude of modern aircraft made such efforts almost useless, stating that Phillips was proposing to "merely revert to a Micawber-like method of ordering them to fly about and wait for something to turn up".
He was interested in her method of ordering them.
A method of second-order accuracy is described for integrating the equations of ideal compressible flow.
The substrate inhibition biokinetics at the optimal conditions were also evaluated using a method of fourth-order Runge Kutta approximation.
