Space Time Method for Solving KdV and KdV-Burgers’ Equation

Korteweg-de Vries equation and KdV-Burgers’ equation are important nonlinear evolutionary equations widely used in engineering and mathematics. These equations have a nonlinear term which makes such problems very complex, thus, it is hard to obtain a high-precision numerical solution. This paper compares the space-time polynomial particular solutions method (ST-MPPS) with the Fourier spectral method to solve the KdV and KdV-Burgers’ equation for different final time. Numerical experiments demonstrate that the space-time polynomial particular solutions method has high precision and robustness when solving dispersion and nonlinear scattering problems.