The Numerical Analysis of Two-Sided Space-Fractional Wave Equation with Improved Moving Least-Square Ritz Method

被引：3
作者：
Cheng, Rongjun [1 ]
Ge, Hongxia [1 ]
Wu, Yong [2 ]
机构：
[1] Ningbo Univ, Fac Maritime & Transportat, Ningbo 315211, Zhejiang, Peoples R China
[2] Zhejiang Univ, Ningbo Inst Technol, Ningbo 315100, Zhejiang, Peoples R China
来源：
MATHEMATICAL PROBLEMS IN ENGINEERING | 2016年 / 2016卷
关键词：
ELEMENT-FREE GALERKIN; FREE METHOD BEFM; DIFFUSION-EQUATIONS; DIFFERENCE-METHODS; APPROXIMATIONS; DERIVATIVES;
D O I：
10.1155/2016/4893724
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
A numerical analysis of the space-fractional wave equation is carried out by the improved moving least-square Ritz (IMLS-Ritz) method. The trial functions for the space-fractional wave equation are constructed by the IMLS approximation. By the Galerkin weak form, the energy functional is formulated. Employing the Ritz minimization procedure, the final algebraic equations system is obtained. In this numerical analysis, the applicability and efficiency of the IMLS-Ritz method are examined by some example problems. Comparing the numerical results with the analytical solutions, the stability and accuracy of the IMLS-Ritz method are also presented.
引用
收藏
页数：9
相关论文
共 56 条
[21]   θ schemes for finite element discretization of the space-time fractional diffusion equations [J].
Guan, Qingguang ;
Gunzburger, Max .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 288 :264-273
[22]   Approximate analytical solution for seepage flow with fractional derivatives in porous media [J].
He, JH .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 167 (1-2) :57-68
[23]   Fast finite difference methods for space-fractional diffusion equations with fractional derivative boundary conditions [J].
Jia, Jinhong ;
Wang, Hong .
JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 :359-369
[24]   On the numerical solutions for the fractional diffusion equation [J].
Khader, M. M. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (06) :2535-2542
[25]   A boundary element-free method (BEFM) for three-dimensional elasticity problems [J].
Kitipornchai, S ;
Liew, KM ;
Cheng, Y .
COMPUTATIONAL MECHANICS, 2005, 36 (01) :13-20
[26]   Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems [J].
Liew, KM ;
Cheng, YM ;
Kitipornchai, S .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2006, 65 (08) :1310-1332
[27]   hp-Meshless cloud method [J].
Liszka, TJ ;
Duarte, CAM ;
Tworzydlo, WW .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 139 (1-4) :263-288
[28]   Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation [J].
Liu, F. ;
Zhuang, P. ;
Anh, V. ;
Turner, I. ;
Burrage, K. .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (01) :12-20
[29]   REPRODUCING KERNEL PARTICLE METHODS [J].
LIU, WK ;
JUN, S ;
ZHANG, YF .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 1995, 20 (8-9) :1081-1106
[30]  
Mainardi F., 2005, NONLINEAR WAVES SOLI, P93
123456