A Meshfree Quasi-Interpolation Method for Solving Burgers' Equation

被引:8
作者
Li, Mingzhu [1 ,2 ]
Chen, Lijuan [1 ]
Ma, Qiang [2 ]
机构
[1] Qingdao Technol Univ, Sch Sci, Qingdao 266033, Peoples R China
[2] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China
关键词
FINITE-ELEMENT APPROACH; NUMERICAL-SOLUTION; COLLOCATION METHOD;
D O I
10.1155/2014/492072
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The main aim of this work is to consider a meshfree algorithm for solving Burgers' equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.
引用
收藏
页数:8
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