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

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).