An Improved Element-Free Galerkin Method for a Kind of KdV Equations
An improved element-free Galerkin method is presented for the numerical solution of the third-order nonlinear KdV equation by coupling the interpolating moving least-squares (IMLS) method with the Galerkin method. The shape function of the IMLS method satisfies the property of Kronecker Delta function, and then the essential boundary condition can be applied directly and easily without any additional numerical effort. A variational method is used to obtain the discrete equations. A numerical example is given to demonstrate the effectiveness of the method presented in this paper for KdV equation.
Di Zheng, Yiqiang Wang, Yi-Min Deng, Aibing Yu and Weihua Li
F. X. Sun and J. F. Wang, "An Improved Element-Free Galerkin Method for a Kind of KdV Equations", Applied Mechanics and Materials, Vols. 101-102, pp. 471-474, 2012