A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation

作者：Shokri Ali; Dehghan Mehdi^*

来源：Computer Physics Communications, 2010, 181(12): 1990-2000.

DOI：10.1016/j.cpc.2010.08.035

• Boussinesq equation (Bq)
• Improved Boussinesq equation (IBq)
• Radial basis functions (RBFs)
• Multiquadrics (MQ)
• Collocation
• Predictor-corrector scheme
• Not-a-Knot method
• Meshless method

A numerical simulation of the improved Boussinesq (IBq) equation is obtained using collocation and approximating the solution by radial basis functions (RBFs) based on the third-order time discretization. To avoid solving the nonlinear system, a predictor-corrector scheme is proposed and the Not-a-Knot method is used to improve the accuracy in the boundary. The method is tested on two problems taken from the literature: propagation of a solitary wave and interaction of two solitary waves. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the new scheme presented in this paper.

• 出版日期2010-12