On the solution of time-fractional KdV-Burgers equation using Petrov-Galerkin method for propagation of long wave in shallow water

In the present article, Petrov-Galerkin method has been utilized for the numerical solution of nonlinear time-fractional KdV-Burgers (KdVB) equation. The nonlinear KdV-Burgers equation has been solved numerically through the Petrov-Galerkin approach utilising a quintic B-spline function as the trial function and a linear hat function as the test function . The numerical outcomes are observed in good agreement with exact solutions for classical order. In case of fractional order, the numerical results of KdV-Burgers equations are compared with those obtained by new method proposed in [1]. Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear dispersive and dissipative problems like the time-fractional KdV-Burgers equation.