A Quadratic B-Spline Galerkin Approach for Solving a Coupled KDV Equation

Abstract

In this paper, a quadratic B-spline Galerkin finite element approach is applied to one-dimensional coupled KdV equation in order to obtain its numerical solutions. The performance of the method is examined on three test problems. Computed results are compared with the exact results and also other numerical results given in the literature. A Fourier stability analysis of the approach is also done.

A numerical treatment based on Haar wavelets for coupled KdV equation

“…By using collocation method and quintic splines Ismail [16] solved cKdV system. A quadratic B-spline Galerkin approach applied by Kutluay and Ucar [17] for solving cKdV system. Ismail and Ashi [18] used a Petrov-Galerkin method and product approximation technique to solve numerically the Hirota-Satsuma cKdV equation.…”

A Numerical Solution for Hirota-Satsuma Coupled KdV Equation

“…Wazwaz [14] produced a finite difference scheme for the periodic initial boundary problem of the CKdV system. Ismail [6] solved this system using collocation method and quintic splines; Kutluay and Ucar [15] solved this system using a quadratic B-spline Galerkin approach.…”

Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model

“…Refs. [1,20,21] and references therein for more information on B-spline FEM. The convergence rate for the finite difference solution of the BBMB equation in the L ∞norm was found to be about second-order, and error estimates showed that the actual error is lower than for the quadratic B-spline FEM [26].…”

“…On the other hand, B-spline basis functions of various degrees can at least achieve C 1 -continuity globally, and so are often used in the numerical solution of PDE -e.g. the quadratic Bspline Galerkin method [1,20,21]. Spectral methods can also be used for discretising the BBMB equation, but we prefer a lower-order method.…”