Abstract
In this article, we have obtained numerical solutions of the modified Kortewegde Vries (MKdV) equation by a numerical technique attributed on subdomain finite element method using quartic B-splines. The proposed numerical algorithm is controlled by applying three test problems including single solitary wave, interaction of two and three solitary waves. To inspect the performance of the newly applied method, the error norms, L2 and L1, as well as the four lowest invariants, I1,I2; I3 and I4, have been computed. Linear stability analysis of the algorithm is also examined.
Highlights
IntroductionSome important physical phenomena for example propagation of long waves in shallow water waves, bubbleliquid mixtures, ion acoustic plasma waves and wave phenomena in enharmonic crystals can be described by the Korteweg de-Vries (KdV) equation which was first suggested by Korteweg and de Vries [1]
The modified Korteweg de-Vries (MKdV) equation which will be studied in this article is related to the following Korteweg de-Vries (KdV) equationUt + εU Ux + μUxxx = 0. (1)The terms U Ux and Uxxx in the Eq(1) represent the nonlinear convection and dispersion, respectively
Some important physical phenomena for example propagation of long waves in shallow water waves, bubbleliquid mixtures, ion acoustic plasma waves and wave phenomena in enharmonic crystals can be described by the KdV equation which was first suggested by Korteweg and de Vries [1]
Summary
Some important physical phenomena for example propagation of long waves in shallow water waves, bubbleliquid mixtures, ion acoustic plasma waves and wave phenomena in enharmonic crystals can be described by the KdV equation which was first suggested by Korteweg and de Vries [1]. Zabusky and Kruskal solved the KdV equation numerically using the finite difference method [4]. Many researches have used various numerical methods including finite difference method [6, 7], finite element method [8,9,10,11,12,13,14,15,16,17,18], pseudospectral method [3] and heat balance integral method [19] to solve the equation. MKdV equation is a special case of the generalized Korteweg de-Vries (GKdV) equation having the form
Sign-in/Register to view highlights & summary 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: Statistics, Optimization & Information Computing
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.
