A Class of P-Stable Hybrid Linear Multistep Methods with Minimal Phase-Lag Error for Second Order Initial Value Problems

By Isaac Felix

Master's Thesis from the year 2018 in the subject Mathematics - Miscellaneous, grade: 82.0%, University of Benin, language: English, abstract: P-stable hybrid linear multistep methods (HLMMs) have been an interesting focus for the numerical solution of second order initial value problems (IVPs) in ordinary di_erential equations (ODEs), because of their high order of accuracy. In this thesis, we present a new class of P-stable HLMMs with order p = 2 and p = 4 respectively for the numerical solution of second order systems. The hybrid schemes which are obtained via Pade 0 approximation approach have minimum Phase-lag error. Numerical experiments are carried out to show the accuracy of the proposed schemes. Nevertheless, the desire in this work is on high order P-stable schemes (p > 4). We give a proposition with proof, stating the limitation of the approach in search for higher order P-stable formulas. Key words: P-stability, Phase-lag error (PLE) constant, Hybrids, order, Interval of periodicity, Pade 0 approximation, Principal local truncation error (PLTE).

• Format: Paperback
• Language: English
• ISBN: 3668811431
• ISBN13: 9783668811430
• Release Date: October 2018
• Publisher: Grin Verlag
• Length: 64 Pages
• Weight: 0.21 lbs.
• Dimensions: 0.1" x 5.8" x 8.3"