Numerical simulations of Kuramoto-Sivashinsky equation in reaction-diffusion via Galerkin method

Finite element methods have been frequently employed in seeking the numerical solutions of PDEs. In this study, a Galerkin finite element numerical scheme is constructed to explore numerical solutions of the generalized Kuramoto-Sivashinsky (gKS) equation. A quartic trigonometric tension (QTT) B-spline function is adapted as base of the Galerkin technique. The incorporation of B-spline Galerkin in space discretization generates the time-dependent system. Then, the use of Crank-Nicolson time integration algorithm to this system gives the wholly discretized scheme. The efficiency of the method is tested over several initial boundary value problems. In addition, the stability of the computational scheme is analyzed by considering Von Neumann technique. The computational results obtained by the suggested scheme are simulated and compared with the commonly existing numerical findings.