Article

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

Rabia SattarDepartment of Mathematics and Statistics, University of Lahore, Lahore, PakistanMuhammad AhmadDepartment of Mathematics and Statistics, University of Lahore, Lahore, PakistanAnjum PervaizDepartment of Mathematics, University of Engineering and Technology, Lahore, PakistanNauman AhmedDepartment of Mathematics and Statistics, University of Lahore, Lahore, PakistanAli AkgülDepartment of Mathematics, Art and Science Faculty, Siirt University, Siirt, Turkey + Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, IndiaSherzod AbdullaevFaculty of Chemical Engineering, New Uzbekistan University, Tashkent, Uzbekistan + Department of Science and Innovation, Tashkent State Pedagogical University named after Nizami, Tashkent, UzbekistanNoorhan F. AlShaikh MohammadDepartment of Physics, Faculty of Applied Science, Palestine Technical University-Kadoorie, Tulkarm, PalestineRania WannanDepartment of Applied Mathematics, Faculty of Applied Science, Palestine Technical University- Kadoorie, Tulkarm, PalestineJihad AsadDepartment of Physics, Faculty of Applied Science, Palestine Technical University-Kadoorie, Tulkarm, Palestine

Thermal Sciencejournal2023en

ABI

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.

Topics

Numerical methods for differential equations Fractional Differential Equations Solutions Differential Equations and Numerical Methods

Identifiers

DOI: 10.2298/tsci2304155s

Citations and references

Cited by 031 references

Metrics — AkademScholar · Coming soon