Quartic B-spline Galerkin approach to the numerical solution of the KdVB equation

The nonlinear Korteweg-de Vries–Burgers’ equation is solved numerically by method of Galerkin using quartic B-splines as both shape and weight functions over the finite intervals. Five test problems are studied to demonstrate the accuracy and efficiency of the proposed method. A comparison of numerical results of both algorithm and some published articles is done in computational section. The numerical results are found in good agreement with exact solutions.