Abstract
The time-fractional coupled Korteweg–de Vries equations (TFCKdVEs) describe various interesting real-world phenomena including wave propagation and the description of shallow water waves on a viscous fluid. This paper presents an accurate and robust numerical technique to solve the TFCKdVE. The cubic B-spline is introduced as a basis function and a quadratic B-spline is used as a test function in a finite element method (FEM) is known as Petrov–Galerkin method. The temporal fractional part is simplified via L1 formula, while the B-spline is employed for the space approximation. The Lax–Richtmyer stability criterion is applied to analyze the stability of the proposed scheme. Four test problems are solved to check performance and validation of the scheme. The accuracy and efficiency of the proposed method are checked via various error norms. The obtained results show good agreement with the exact solutions and earlier work available in the literature.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
