THERMAL SCIENCE

International Scientific Journal

Rabia Sattar

,

Muhammad Ozair Ahmad

,

Anjum Pervaiz

,

Nauman Ahmed

,

Ali Akgül

,

Sherzod Abdullaev

,

Noorhan Alshaikh

,

Rania Wannan

,

Jihad Asad

NON-POLYNOMIAL CUBIC SPLINE METHOD USED TO FATHOM SINE GORDON EQUATIONS IN 3+1 DIMENSIONS

ABSTRACT
This study contains an algorithmic solution of the Sine Gordon equation in three space and time dimensional problems. For discretization, the central difference formula is used for the time variable. In contrast, space variable x, y, and z are discretized using the non-polynominal cubic spline functions for each. The proposed scheme brings the accuracy of order O(h2 + k2 + σ2 + τ2h2 + τ2k2 + τ2σ2) by electing suitable parametric values. The paper also discussed the truncation error of the proposed method and obtained the stability analysis. Numerical problems are elucidated by this method and compared to results taken from the literature.
KEYWORDS
Sine gordon equation, 3-D wave equations, truncation error, non-polynomial cubic spline function, stability analysis
PUBLISHED ONLINE: 2023-09-17
DOI REFERENCE: https://doi.org/10.2298/TSCI2304155S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 4, PAGES [3155 - 3170]
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Non-polynomial cubic spline method used to fathom Sine Gordon equations in 3+1 dimensions

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence