A comparative study between two different methods for solving the general Korteweg–de Vries equation (GKdV)

The family of the KdV equations, the most famous equations embodying both nonlinearity and dispersion, has attracted enormous attention over the years and has served as the model equation for the development of soliton theory. In this paper we present a comparative study between two different methods for solving the general KdV equation, namely the numerical Crank Nicolson method, and the semi-analytic Adomian decomposition method. The stability of the numerical Crank Nicolson scheme is discussed. A comparison between the two methods is carried out to illustrate the pertinent features of the two algorithms.