期刊
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 39, 期 7, 页码 1820-1835出版社
WILEY
DOI: 10.1002/mma.3604
关键词
spectral meshless radial point interpolation (SMRPI) method; radial basis function; time-fractional derivatives; finite differences
H. Ammari In this article, an innovative technique so-called spectral meshless radial point interpolation (SMRPI) method is proposed and, as a test problem, is applied to a classical type of two-dimensional time-fractional telegraph equation defined by Caputo sense for (1 < 2). This new methods is based on meshless methods and benefits from spectral collocation ideas, but it does not belong to traditional meshless collocation methods. The point interpolation method with the help of radial basis functions is used to construct shape functions, which play as basis functions in the frame of SMRPI method. These basis functions have Kronecker delta function property. Evaluation of high-order derivatives is not difficult by constructing operational matrices. In SMRPI method, it does not require any kind of integration locally or globally over small quadrature domains, which is essential of the finite element method (FEM) and those meshless methods based on Galerkin weak form. Also, it is not needed to determine strict value for the shape parameter, which plays an important role in collocation method based on the radial basis functions (Kansa's method). Therefore, computational costs of SMRPI method are less expensive. Two numerical examples are presented to show that SMRPI method has reliable rates of convergence. Copyright (c) 2015 John Wiley & Sons, Ltd.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据