Stability Ordinates of Adams Predictor-Corrector Methods
نویسندگان
چکیده
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 stability ordinate, also known as the imaginary stability boundary. It has previously been shown that exactly half of Adams-Bashforth, Adams-Moulton, 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 p is the order of the method, ABp-AMp methods have nonzero stability ordinate 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, . . ..
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