A mesh-free numerical method for solution of the family of Kuramoto-Sivashinsky equations

作者：Uddin Marjan^*; Haq Sirajul; Siraj ul Islam

来源：Applied Mathematics and Computation, 2009, 212(2): 458-469.

DOI：10.1016/j.amc.2009.02.037

• Radial basis RBFs)
• Mesh-free interpolation method
• Kuramoto-Sivashinsky (KS) equations

In this paper, radial basis RBFs) based mesh-free method is implemented to find numerical solution of the Kuramoto-Sivashinsky equations. This approach has an edge over traditional methods such as finite-difference and finite element methods because it does not require a mesh to discretize the problem domain, and a set of scattered nodes in the domain of influence provided by initial data is required for the realization of the method. The accuracy of the method is assessed in terms of the error norms L(2); L(infinity), number of nodes in the domain of influence, free parameter, dependent parameter RBFs and time step length. Numerical experiments demonstrate accuracy and robustness of the method for solving a class of nonlinear partial differential equations.

• 出版日期2009-6-15