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.

在寻求PDE的数值解时，经常采用有限元方法。在这项研究中，构造了Galerkin有限元数值格式，以探索广义Kuramoto-Sivashinsky（gKS）方程的数值解。四次三角张力（QTT）B样条函数被改编为Galerkin技术的基础。B样条Galerkin在空间离散化中的结合产生了时间相关的系统。然后，对该系统使用Crank-Nicolson时间积分算法可得出完全离散的方案。在几个初始边界值问题上测试了该方法的效率。另外，通过考虑冯·诺依曼技术来分析计算方案的稳定性。