Stability ordinates of Adams predictor-corrector methods

作者：Ghrist Michelle L^*; Fornberg Bengt; Reeger Jonah A

来源：BIT Numerical Mathematics, 2015, 55(3): 733-750.

DOI：10.1007/s10543-014-0528-7

• Adams methods
• Predictor-corrector
• Imaginary stability boundary
• Linear multistep methods
• Finite difference methods
• Stability region
• Stability ordinate

How far the stability domain of a numerical method for approximating solutions to differential equations extends along the imaginary axis indicates how useful the method is for approximating solutions to wave equations; this maximum extent is termed the imaginary stability boundary, also known as the stability ordinate. It has previously been shown that exactly half of Adams-Bashforth (AB), Adams-Moulton (AM), and staggered Adams-Bashforth methods have nonzero stability ordinates. In this paper, we consider two categories of Adams predictor-corrector methods and prove that they follow a similar pattern. In particular, if is the order of the method, AB-AM methods have nonzero stability ordinate only for , and AB(1)-AM methods have nonzero stability ordinates only for p = 1, 2, 5, 6, 9, 10, ... , and AB(p-1)-AMp methods have nonzero stability ordinates only for p = 3, 4, 7, 8, 11, 12, ... .

• 出版日期2015-9
• 单位中国人民解放军空军电子技术研究所