On Ninth Order, Explicit Numerov-Type Methods with Constant Coefficients

A new family of effectively nine stages, ninth-order hybrid explicit Numerov-type methods is presented for the solution of some special second order Initial Value Problem. After dealing with a reduced set of order conditions, we derive an optimal constant coefficients method along with a similar kin...

Full description

Saved in:
Bibliographic Details
Published in:Mediterranean journal of mathematics 2018-04, Vol.15 (2), p.1-17, Article 46
Main Authors: Tsitouras, Ch, Simos, T. E.
Format: Article
Language:English
Subjects:
Boundary value problems
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A new family of effectively nine stages, ninth-order hybrid explicit Numerov-type methods is presented for the solution of some special second order Initial Value Problem. After dealing with a reduced set of order conditions, we derive an optimal constant coefficients method along with a similar kind of method with reduced phase errors. We proceed with numerical tests using quadruple precision arithmetic on some well-known problems from the relevant literature. Finally, in the appendices, we list Mathematica packages implementing the corresponding algorithms.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-018-1089-9