Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques.
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| Title: | Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques. |
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| Authors: | S, Kumbinarasaiah1 (AUTHOR) kumbinarasaiah@gmail.com, Veeresha, P.2 (AUTHOR), Prakasha, D. G.3 (AUTHOR), Malagi, N. S.4 (AUTHOR), Ramane, H. S.5 (AUTHOR), Pise, K. S.5 (AUTHOR) |
| Source: | International Journal of Modelling & Simulation. Oct2026, Vol. 46 Issue 5, p1614-1634. 21p. |
| Subjects: | Sine-Gordon equation, Newton-Raphson method, Laplace transformation, Nonlinear wave equations, Scientific method, Error analysis in mathematics |
| Abstract: | In this work, we obtained a new functional matrix using Clique-polynomials of complete graphs $\left({{K_n}} \right)$ K n with $n$ n vertices and considered a new approach to solving the Sine–Gordon (SG) equation. The clique polynomial method transforms this equation into a system of algebraic equations. The solution will be drawn with the help of Newton Raphson's method. Also, we employed the q-homotopy analysis transform method (q-HATM), which is the proper collision of the Laplace transform and the q-homotopy analysis method (q-HAM). To witness the reliability and accuracy of the considered schemes, some illustrations of the SG equation and double SG equation are considered. Here, the SG equation is solved easily and elegantly without using discretization or transformation of the equation by using the q-HATM. Also, in q-HATM, the presence of homotopy and axillary parameters allows us to have a large convergence region. The 3D surfaces of acquired solutions are drawn effectively. The tables of error analysis demonstrate the success of these methods. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Modelling & Simulation is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 197554487 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22S%2C+Kumbinarasaiah%22">S, Kumbinarasaiah</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kumbinarasaiah@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Veeresha%2C+P%2E%22">Veeresha, P.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Prakasha%2C+D%2E+G%2E%22">Prakasha, D. G.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Malagi%2C+N%2E+S%2E%22">Malagi, N. S.</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ramane%2C+H%2E+S%2E%22">Ramane, H. S.</searchLink><relatesTo>5</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Pise%2C+K%2E+S%2E%22">Pise, K. S.</searchLink><relatesTo>5</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Modelling+%26+Simulation%22">International Journal of Modelling & Simulation</searchLink>. Oct2026, Vol. 46 Issue 5, p1614-1634. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Sine-Gordon+equation%22">Sine-Gordon equation</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Laplace+transformation%22">Laplace transformation</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+wave+equations%22">Nonlinear wave equations</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+method%22">Scientific method</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work, we obtained a new functional matrix using Clique-polynomials of complete graphs $\left({{K_n}} \right)$ K n with $n$ n vertices and considered a new approach to solving the Sine–Gordon (SG) equation. The clique polynomial method transforms this equation into a system of algebraic equations. The solution will be drawn with the help of Newton Raphson's method. Also, we employed the q-homotopy analysis transform method (q-HATM), which is the proper collision of the Laplace transform and the q-homotopy analysis method (q-HAM). To witness the reliability and accuracy of the considered schemes, some illustrations of the SG equation and double SG equation are considered. Here, the SG equation is solved easily and elegantly without using discretization or transformation of the equation by using the q-HATM. Also, in q-HATM, the presence of homotopy and axillary parameters allows us to have a large convergence region. The 3D surfaces of acquired solutions are drawn effectively. The tables of error analysis demonstrate the success of these methods. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Modelling & Simulation is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/02286203.2024.2400658 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 1614 Subjects: – SubjectFull: Sine-Gordon equation Type: general – SubjectFull: Newton-Raphson method Type: general – SubjectFull: Laplace transformation Type: general – SubjectFull: Nonlinear wave equations Type: general – SubjectFull: Scientific method Type: general – SubjectFull: Error analysis in mathematics Type: general Titles: – TitleFull: Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: S, Kumbinarasaiah – PersonEntity: Name: NameFull: Veeresha, P. – PersonEntity: Name: NameFull: Prakasha, D. G. – PersonEntity: Name: NameFull: Malagi, N. S. – PersonEntity: Name: NameFull: Ramane, H. S. – PersonEntity: Name: NameFull: Pise, K. S. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02286203 Numbering: – Type: volume Value: 46 – Type: issue Value: 5 Titles: – TitleFull: International Journal of Modelling & Simulation Type: main |
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