Order and effective order

✍ Scribed by J.C. Butcher

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 834 KB
• Volume: 28
• Category: Article
• ISSN: 0168-9274
• DOI: 10.1016/s0168-9274(98)00043-9

✦ Synopsis

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. o 1998 Elsevier Science B.V. and IMACS. All rights reserved.