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


Master's Thesis, 2018

57 Pages, Grade: 82.0%


Abstract or Introduction

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).

Details

Title
A Class of P-Stable Hybrid Linear Multistep Methods with Minimal Phase-Lag Error for Second Order Initial Value Problems
College
University of Benin
Grade
82.0%
Author
Year
2018
Pages
57
Catalog Number
V442178
ISBN (eBook)
9783668811423
ISBN (Book)
9783668811430
Language
English
Tags
class, p-stable, hybrid, linear, multistep, methods, minimal, phase-lag, error, second, order, initial, value, problems
Quote paper
Isaac Felix (Author), 2018, A Class of P-Stable Hybrid Linear Multistep Methods with Minimal Phase-Lag Error for Second Order Initial Value Problems, Munich, GRIN Verlag, https://www.grin.com/document/442178

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