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- Title
On the applications of collocation method for numerically analyzing the nonlinear Degasperis–Procesi and Benjamin–Bona–Mahony equations.
- Authors
Ahmad, Iftikhar; Ibrar Hussain, Syed; Ilyas, Hira; Jabeen, Shazia; Iqrar, Asma
- Abstract
This research uses the Sinc Collocation method to numerically examine the Degasperis–Procesi and Benjamin–Bona–Mahony equations, achieving a high level of precision and accuracy on computational grounds with a variety of mesh points. The proposed technique involves global collocation using Sinc bases function (SBF) as an activation function. Initially, the time derivative discretization has been performed through finite difference scheme and the remaining spatial derivatives are approximated by θ -weighted scheme to minimize the complexity in numerical computations. The main contribution of research is in modifying the proposed scheme to overcome the complexity involved in the whole process of finding solutions with a cardinal expansion of Sinc functions in nonlinear and singular systems. The solutions of Degasperis–Procesi and Benjamin–Bona–Mahony stiff nonlinear systems are illustrated numerically and graphically and the validation and verification of the obtained results are examined through stability analysis by calculating the spectral radius by bounding the value of θ. A comparative study is presented with some of the well-known numerical techniques, which assured the accuracy and reliability of our technique.
- Subjects
GALERKIN methods; EQUATIONS; COLLOCATION methods; FINITE differences; MATHEMATICAL bounds; NONLINEAR systems; NONLINEAR functions
- Publication
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics, 2024, Vol 38, Issue 20, p1
- ISSN
0217-9792
- Publication type
Article
- DOI
10.1142/S0217979224502643