2024 : 11 : 13

Mohammad Mehdizadeh

Academic rank: Professor
ORCID:
Education: PhD.
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Faculty: 1
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Research

Title
An explicit six-step singularly P-stable Obrechkoffmethod for the numerical solution of second-orderoscillatory initial value problems
Type
JournalPaper
Keywords
Explicit methods·Phase-lag·Ordinary differential equations·Singularly P-stable·Symmetric multistep methods
Year
2020
Journal NUMERICAL ALGORITHMS
DOI
Researchers Mohammad Mehdizadeh ، Ali Shokri Shokri

Abstract

In this paper, we present an explicit six-step singularly P-stable Obrechkoff methodof tenth algebraic order for solving second-order linear periodic and oscillatory initialvalue problems of ordinary differential equations. The advantage of this new singu-larly P-stable Obrechkoff method is that it is a high-order explicit method, and thusdoes not require additional predictor stages. The numerical stability and phase prop-erties of the new method is analyzed. Four numerical examples show that the newexplicit method is more accurate than Obrechkoff schemes of the same order whenapplied to the numerical solution of second-order initial value problems with highlyoscillatory solutions.