Non-polynomial cubic spline method used to fathom Sine Gordon equations in 3+1 dimensions-Reference-Cited by-同舟云学术

Non-polynomial cubic spline method used to fathom Sine Gordon equations in 3+1 dimensions

Published:2023 Issue:4 Part B Volume:27 Page:3155-3170
ISSN:0354-9836
Container-title:Thermal Science
language:en
Short-container-title:THERM SCI

Author:

Sattar Rabia¹,Ahmad Muhammad¹,Pervaiz Anjum²,Ahmed Nauman¹,Akgul Ali³,Abdullaev Sherzod⁴,Alshaikh Noorhan⁵,Wannan Rania⁶,Asad Jihad⁵

Affiliation:

1. Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan

2. Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan

3. Department of Mathematics, Art and Science Faculty, Siirt University, Siirt, Turkey + Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India

4. Faculty of Chemical Engineering, New Uzbekistan University, Tashkent, Uzbekistan + Department of Science and Innovation, Tashkent State Pedagogical University named after Nizami, Tashkent, Uzbekistan

5. Department of Physics, Faculty of Applied Science, Palestine Technical University-Kadoorie, Tulkarm, Palestine

6. Department of Applied Mathematics, Faculty of Applied Science, Palestine Technical University- Kadoorie, Tulkarm, Palestine

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 + ?2 + ?2h2 + ?2k2 + ?2?2) 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.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

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