ON THE CONSTRUCTION OF p-STABLE HYBRID MULTISTEP METHODS FOR SECOND ORDER ODEs

A New Symmetric p-stable Obrechkoff Method with Optimal Phase lag for Oscillatory Problems

“…-stable Obrechkoff Method with Optimal Phase-lag … 115 also the works in[7,8,10]. In particular, the new results in this article enjoy considerable order of accuracy and stronger p-stability property which are illustrated in Table1andFigures 1,4,5,6, respectively.…”

“…Unlike other stability requirements, 2-step p-stable methods remain desirable for the solution of (1). There is vast literature on approximate solution of (1), see [7], [8], [9], [10], [11], [31], [32], [3][4][5], [2], [24][25][26][27], [6], [11], [32], [28][29][30], [10], [35][36][37], [20], [33]. The significance of this present work is five-fold; (i) to illustrate the strength of PAA in the development of numerical methods capable of handling IVPs that are periodic in nature, (ii) derive new p-stable methods and investigate their phase-lag properties, (iii) provide useful insight on p-stable Obrechkoff methods, (iv) remark that "direct application of PAA framework" on the development of p-stable numerical methods will often be limited to schemes of order , 4 ≤ p (v) wide application of the derived methods.…”