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

被引：0

作者：

Sattar, Rabia ^{[1
]}

Ahmad, Muhammad Ozair ^{[1
]}

Pervaiz, Anjum ^{[2
]}

Ahmed, Nauman ^{[1
]}

Akgul, Ali ^{[3
,4
]}

Abdullaev, Sherzod ^{[5
,6
]}

Alshaikh, Noorhan ^{[7
]}

Wannan, Rania ^{[8
]}

Asad, Jihad ^{[7
]}

机构：

[1] Univ Lahore, Dept Math & Stat, Lahore, Pakistan

[2] Univ Engn & Technol, Dept Math, Lahore, Pakistan

[3] Siirt Univ, Art & Sci Fac, Dept Math, Siirt, Turkiye

[4] SIMATS, Saveetha Sch Engn, Dept Elect & Commun Engn, Chennai, Tamil Nadu, India

[5] New Uzbekistan Univ, Fac Chem Engn, Tashkent, Uzbekistan

[6] Tashkent State Pedag Univ, Dept Sci & Innovat, Tashkent, Uzbekistan

[7] Palestine Tech Univ Kadoorie, Fac Sci Appl, Dept Phys, Tulkarm, Palestine

[8] Palestine Tech Univ Kadoorie, Fac Sci Appl, Dept Appl Math, Tulkarm, Palestine

来源：

THERMAL SCIENCE | 2023年 / 27卷 / 4B期

关键词：

Sine gordon equation; 3-D wave equations; truncation error; non-polynomial cubic spline function; stability analysis; NUMERICAL-SOLUTION;

D O I：

10.2298/TSCI2304155S

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

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(h(2) + k(2) + sigma(2) + iota(2)h(2) + iota(2)k(2) + iota(2)sigma(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.

引用

页码：3155 / 3170

页数：16

共 14 条

[1] Non-polynomial Cubic Spline Method for Three-Dimensional Wave Equation
Sattar R.
Ahmad M.O.
Pervaiz A.
Ahmed N.
Akgül A.
International Journal of Applied and Computational Mathematics, 2023, 9 (6)
[2] Cubic B-spline method for non-linear sine-Gordon equation
Singh, Suruchi
Singh, Swarn
Aggarwal, Anu
COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (08)
[3] Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term
Zadvan, Homa
Rashidinia, Jalil
NUMERICAL ALGORITHMS, 2017, 74 (02) : 289 - 306
[4] Cubic B-spline method for non-linear sine-Gordon equation
Suruchi Singh
Swarn Singh
Anu Aggarwal
Computational and Applied Mathematics, 2022, 41
[5] Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term
Homa Zadvan
Jalil Rashidinia
Numerical Algorithms, 2017, 74 : 289 - 306
[6] A new non-polynomial spline method for solution of linear and non-linear third order dispersive equations
Sultana, Talat
Khan, Arshad
Khandelwal, Pooja
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[7] A new non-polynomial spline method for solution of linear and non-linear third order dispersive equations
Talat Sultana
Arshad Khan
Pooja Khandelwal
Advances in Difference Equations, 2018
[8] Cubic non-polynomial spline on piecewise mesh for singularly perturbed reaction differential equations with robin type boundary conditions
Esayas Ayele, Bethelhem
Bullo, Tesfaye Aga
Duressa, Gemechis File
BMC RESEARCH NOTES, 2025, 18 (01)
[9] A new variable mesh method based on non-polynomial spline in compression approximations for 1D quasilinear hyperbolic equations
Mohanty, Ranjan Kumar
Jha, Navnit
Kumar, Ravindra
ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[10] Fourth order computational method for two parameters singularly perturbed boundary value problem using non-polynomial cubic spline
Phaneendra, K.
Mahesh, G.
INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS, 2019, 10 (03) : 261 - 275

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