Abstract
In this research work, we examine the Korteweg-de Vries equation (KdV), which is utilized to formulate the propagation of water waves and occurs in different fields such as hydrodynamics waves in cold plasma acoustic waves in harmonic crystals. This research presents two efficient computational methods based on Legendre wavelets to solve the Korteweg-de Vries. The three-step Taylor method is first applied to the Korteweg-de Vries equation for time discretization. Then, the Galerkin and collocation methods are used for spatial discretization. With these approaches, bringing the approximate solutions of the Korteweg-de Vries equation turns into getting the solution of the algebraic equation system. The solution of this system gives the Legendre wavelet coefficients. The approximate solution can be obtained by substituting the obtained coefficients into the Legendre wavelet series expansion. The presented wavelet methods are tested by studying different problems at the end of this study.
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 callMore From: Turkish Journal of Mathematics and Computer Science
Disclaimer: 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.
