Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques
- Title
- Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques
- Creator
- S K.; Veeresha P.; Prakasha D.G.; Malagi N.S.; Ramane H.S.; Pise K.S.
- Description
- In this work, we obtained a new functional matrix using Clique-polynomials of complete graphs (Formula presented.) with (Formula presented.) vertices and considered a new approach to solving the SineGordon (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 Raphsons 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. 2024 Informa UK Limited, trading as Taylor & Francis Group.
- Source
- International Journal of Modelling and Simulation
- Date
- 2024-01-01
- Publisher
- Taylor and Francis Ltd.
- Subject
- Clique-polynomials; Functional matrix; q-homotopy analysis transform method
- Coverage
- S K., Department of Mathematics, Bangalore University, Bengaluru, India; Veeresha P., Department of Mathematics, Christ University, Bangalore, India; Prakasha D.G., Department of Mathematics, Davangere University, Davangere, India; Malagi N.S., Department of Mathematics, Jain College of Engineering and Research, Belagavi, Karnataka, India; Ramane H.S., Department of Mathematics, Karnatak University, Dharwad, India; Pise K.S., Department of Mathematics, Karnatak University, Dharwad, India
- Rights
- Restricted Access
- Relation
- ISSN: 2286203; CODEN: IMSIE
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
S K.; Veeresha P.; Prakasha D.G.; Malagi N.S.; Ramane H.S.; Pise K.S., “Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 25, 2025, https://archives.christuniversity.in/items/show/13476.