A meshless scheme for partial differential equations based on multiquadric trigonometric B-spline quasi-interpolation  

作　　者：高文武 王志刚 

机构地区：[1]School of Economics, Anhui University [2]Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences,Fudan University [3]School of Mathematics and Finance, Fuyang Teachers College

出　　处：《Chinese Physics B》2014年第11期152-156,共5页中国物理B（英文版）

基　　金：supported by the Shanghai Guidance of Science and Technology,China(Grant No.12DZ2272800);the Natural Science Foundation of Education Department of Anhui Province,China(Grant No.KJ2013B203);the Foundation of Introducing Leaders of Science and Technology of Anhui University,China(Grant No.J10117700057)

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 ac- count 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 dif- ficulty 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.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 ac- count 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 dif- ficulty 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.

关 键 词：QUASI-INTERPOLATION meshless collocation PERIODICITY divided difference 

分 类 号：O175.2[理学—数学] O174.42[理学—基础数学]