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.

Ahmad I., Hussain S. I., Ilyas H., Jabeen S., Iqrar A. (2024). On the applications of collocation method for numerically analyzing the nonlinear Degasperis-Procesi and Benjamin-Bona-Mahony equations. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 38(20) [10.1142/S0217979224502643].

On the applications of collocation method for numerically analyzing the nonlinear Degasperis-Procesi and Benjamin-Bona-Mahony equations

Hussain S. I.
;
2024-08-01

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.
ago-2024
Settore MATH-05/A - Analisi numerica
Ahmad I., Hussain S. I., Ilyas H., Jabeen S., Iqrar A. (2024). On the applications of collocation method for numerically analyzing the nonlinear Degasperis-Procesi and Benjamin-Bona-Mahony equations. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 38(20) [10.1142/S0217979224502643].
File in questo prodotto:
File Dimensione Formato  
On_the_applications_of_collocation_method_for_nume.pdf

Solo gestori archvio

Tipologia: Versione Editoriale
Dimensione 1.39 MB
Formato Adobe PDF
1.39 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/672032
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 6
social impact