Numerical Investigation of Separated Solitary Waves Solution for KDV Equation through Finite Element Technique

Abstract

The Present manuscript reports the solution of well known non linear wave mechanics problem called KDV equation, here main emphasis is given on the Mathematical modeling of traveling waves and their solutions in the form of Kortewegde Vries equation (KdV) It is a non-linear Partial Differential Equation (PDE) of third order which arises in a number of physical applications such as water waves, elastic rods, plasma physics etc. We present numerical solution of the above equation using B-spline FEM (Finite Element Method) approach. The ultimate goal of the paper is to solve the above problem using numerical simulation in which the accuracy of computed solutions is examined by making comparison with analytical solutions, which are found to be in good agreement with each other along with that we discussed the physical interpolation of the soliton study in which we found that the travel waves reaches to the maximum magnitude of the velocity in the short time of the interval and there is an uncertainty in the motion of the moving waves. Another important observation we found that the maximum magnitude of the velocity in the most of the time domain is around 1 but in some of the condition waves having a unnatural phenomena which is called the existence of the doubly soliton is seemed frequently. All above observation which is clearly indication of the generic outcome of a weakly nonlinear long-wave asymptotic analysis of many physical systems. The another achievement of the work is to implementation of the cubic Bspline FEM in the above non linear propagating waves phenomena.

Finite element analysis of melting effects on MHD stagnation-point non-Newtonian flow and heat transfer from a stretching/shrinking sheet

“…The version employed herein is a variational formulation which has met with considerable success in recent years in simulating many complex fluid flows. These include thermal radiation-convection micropolar flow [34], mixed convection micropolar flow [35], magneto-hemodynamic non-Newtonian flow [36], nanofluid mechanics [36][37][38] and free surface wave hydrodynamics [39]. In order to apply finite element method first we assume .…”

Double Elzaki Transform Decomposition Method for Solving Third Order Korteweg-De-Vries Equations

“…So many methods and approaches have been made to find the approximate analytic solutions and numerical solutions of KdV equations, such as Adomian Decomposition Method (ADM) [1], Variation Iteration Method (VIM) [1], Homotopy Perturbation Method (HPM) [1], Homotopy Perturbation Method using Elzaki Transform [2], Homotopy Perturbation Method using Laplace Transform [3], Adomian Decomposition Method using Elzaki Transform [4], Numerical solutions to a linear KdV equation on unbounded domain [5], The numerical solutions of KdV equation using radial basis functions [6], Numerical solution of separated solitary waves for KdV equation through finite element technique [7].…”

The Exponential Cubic B-Spline Algorithm for Korteweg-de Vries Equation

“…by Canıvar et al in [17]. A study based on cubic B-spline finite element method for the solution of the KdVE is suggested by Kapoor et al [18]. A Bubnov-Galerkin finite element method with quintic B-spline functions taken as element shape and weight functions is presented for the solution of the KdVE [19].…”