Order and effective order Original Research Article

There has recently been a revival of interest in the concept of “effective order”. In this survey of the subject, we will discuss this generalization of order in its original context of non-stiff ordinary differential equations. We will also look at more recent applications, especially to the solution of stiff problems using singly-implicit methods. It is seen that many of the disadvantages of implicit Runge-Kutta methods can be overcome, first by restricting consideration to singly-implicit methods, and then by weakening the order requirements to effective order.