THERMAL SCIENCE

International Scientific Journal

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Yasir Nawaz

,

Muhammad Arif

A NEW CLASS OF A-STABLE NUMERICAL TECHNIQUES FOR ORDINARY DIFFERENTIAL EQUATIONS: APPLICATION TO BOUNDARY-LAYER FLOW

ABSTRACT
The present attempt is made to propose a new class of numerical techniques for finding numerical solutions of ODE. The proposed numerical techniques are based on interpolation of a polynomial. Currently constructed numerical techniques use the additional information(s) of derivative(s) on particular grid point(s). The advantage of the presently proposed numerical techniques is that these techniques are implemented in one step and can provide highly accurate solution and can be constructed on fewer amounts of grid points but has the disadvantage of finding derivative(s). It is to be noted that the high order techniques can be constructed using just two grid points. Presently proposed fourth order technique is A-stable but not L-stable. The order and maximum absolute error are found for a fourth order technique. The fourth order technique is employed to solve the Darcy-Forchheimer fluid-flow problem which is transformed further to a third-order non-linear boundary value problem on the semi-infinite domain.
KEYWORDS
Interpolation, Darch-Forchheimer flow, A-stable, Maximum absolute error, derivative(s)
PAPER SUBMITTED: 2019-09-26
PAPER REVISED: 2020-01-24
PAPER ACCEPTED: 2020-02-07
PUBLISHED ONLINE: 2020-03-08
DOI REFERENCE: https://doi.org/10.2298/TSCI190926097N
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [1665 - 1675]
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A new class of A-stable numerical techniques for ordinary differential equations: Application to boundary-layer flow

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