Numerical Simulation of KdV-Burgers' Equation in Dusty Plasmas

In this paper, the reductive perturbation method is used to derive the KdV Burgers’ equation in dusty plasmas in the presence of the Boltzmann distribution of electrons and ions and charged dust grains. A numerical solution to the KdV Burgers’ equation has been obtained by using the explicit finite difference method, and the solitary and shock structures have been studied at various values of the dispersion coefficient and the dissipation coefficient. A comparison of solitary and shock structures is also shown by plotting the analytical and numerical solutions. The accuracy and efficiency of the present method have been evaluated by comparing the absolute error of the numerical results obtained with the analytical solution. An analysis of Von Neumann stability is conducted and it shows that the scheme is unconditionally stable.