中国物理B ›› 2014, Vol. 23 ›› Issue (11): 110207-110207.doi: 10.1088/1674-1056/23/11/110207
高文武a b, 王志刚c
Gao Wen-Wu (高文武)a b, Wang Zhi-Gang (王志刚)c
摘要:
Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions.
中图分类号: (Numerical approximation and analysis)