Numerical solution of fourth order generalised Kuramoto-Sivashinsky equation using modified quintic B-spline differential quadrature method

In this paper, numerical solutions of the nonlinear generalised Kuramoto-Sivashinsky equation are presented using a modified quintic B-spline differential quadrature method. The Crank-Nicolson and forward finite difference schemes are applied for discretization, while the Rubin and Graves approach is utilised for linearization. The matrix stability approach is used to analyse the method’s stability. Numerical examples demonstrate the accuracy of the method. The computed results are presented in tables and graphs along with a comparative analysis with previous results. The obtained numerical results demonstrate the method’s reliability and its compatibility with the exact solutions.