Convergence analysis of the finite difference solution for coupled Drinfeld–Sokolov–Wilson system

This paper is devoted to drive the matrix algebraic equation for the coupled Drinfeld–Sokolov–Wilson (DSW) system using the implicit finite difference (IMFD) method. The convergence analysis of the finite difference solution is proved. Numerical experiment is presented with initial conditions describing the generation and evolution. The numerical results were being compared on the basis of calculating the absolute error (ABSE) and the mean square error (MSE). The numerical results proved that the numerical solution was close to the real solution at different values of time.