THERMAL SCIENCE

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Aydin Secer

,

Selvi Altun

A NEW NUMERICAL APPROACH FOR SOLVING HIGH-ORDER LINEAR AND NON-LINEAR DIFFERANTIAL EQUATIONS

ABSTRACT
In this paper, the Legendre wavelet operational matrix method has been introduced for solving high-order linear and non-linear multi-point: initial and boundary value problems. It has been suggested that the technique is rest upon practical application of the operational matrix and its derivatives. The differential equation is presented that it is converted to a system of algebraic equations via the properties of Legendre wavelet together with the operational matrix method. As a result of this study, the scheme has been tested on five linear and non-linear problems. The results have demonstrated that this method is a very effective and advantageous tool in solving such problems.
KEYWORDS
Shifted Legendre polynomials, Legendre wavelet, operational matrix, high order differential equations
PAPER SUBMITTED: 2017-06-12
PAPER REVISED: 2017-11-17
PAPER ACCEPTED: 2017-11-20
PUBLISHED ONLINE: 2018-01-07
DOI REFERENCE: https://doi.org/10.2298/TSCI170612272S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S67 - S77]
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A new numerical approach for solving high-order linear and non-linear differantial equations

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