KdV Equation and Computations of Solitons: Nonlinear Error Dynamics

Here we have developed new compact and hybrid schemes for the solution of KdV equation. These schemes for the third derivative have been analyzed in the spectral plane for their resolution and compared with another scheme in the literature. Furthermore the developed schemes have been used to solve a model linear dispersion equation. The error dynamics equation has been developed for this model equation. Despite the linearity of the model equation, one can draw conclusions for error dynamics of nonlinear differential equations. The developed compact scheme has been found to be quite accurate in solving KdV equation. One- and two-soliton cases have been reported to demonstrate the above.