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Mohammad Mehdizadeh

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

Title
A New Efficient High Order Four-Step Multiderivative Method for the Numerical Solution of Second-Order IVPs with Oscillating Solutions
Type
JournalPaper
Keywords
Phase-lag error; Initial value problems; P-stable; Symmetric multistep methods; Periodicity interval
Year
2020
Journal Mathematics Interdisciplinary Research
DOI
Researchers Ali Shokri Shokri ، Mohammad Mehdizadeh

Abstract

In this paper, we present a new high order explicit four-step method of eighth algebraic order for solving second-order linear periodic and oscillatory initial value problems of ordinary differential equations such as undamped Duffing's equation. Numerical stability and phase properties of the new method is analyzed. The main structure of the method is multiderivative, and the combined phases were applied to expand the stability interval and to achieve P-stability. The advantage of the method in comparison with similar methods in terms of efficiency, accuracy, and stability is shown by its implementation in some well-known problems.