A P-Stable Eighth-Order Method for the Numerical Integration of Periodic Initial-Value Problems

✍ Scribed by T.E. Simos; Ch. Tsitouras

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 254 KB
• Volume: 130
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.5567

✦ Synopsis

Several methods have been developed for the solution of (1) belonging to Category I. We mention the works of An eighth-order P-stable two-step method for the numerical integration of second-order periodic initial-value problems is developed Raptis and Allison [5], Cash, in this paper. This method has seven stages per iteration and an Raptis, and Simos [6], Ixaru and Rizea [7], Simos [8], and interval of periodicity equal to (0, ȍ); i.e., it is P-stable. Numerical Thomas, Simos, and Mitsou [9]. The main disadvantage of and theoretical results obtained for several well-known problems these methods is the requirement of the knowledge a priori show the efficiency of the new method. ᮊ 1997 Academic Press of the frequency of the solution of the problem. The main areas of application of these methods are problems for which the above requirement is possible, such as the