In this paper, we present a novel approach for solving non-linear evolution partial differential equations with mixed initial-boundary conditions. The novelty of this approach is in combination of pseudo- spectral approximation, in particular collocation approximation, and forward Euler scheme in time by means a grid points. The main idea is using pseudo-spectral approximation for decomposing solution on orthogonal basis of functions to obtain nonlinear ordinary differential equation in time variable. Discretization is then performed on time variable using forward Euler scheme to approach the nonlinear term by a polynomial of Lagrange interpolation. Afterwards the investigations on stability and convergence of solution are presented.

pseudo-spectral method, finite difference, Lagrange interpolation, EDPs evolution.