An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)

doi:10.1088/1674-1056/22/6/060210

Abstract A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The exact mathematical result of GFE has been widely used in population dynamics and genetics, where it originated. Many researchers have studied the numerical solutions of GFE, up to now. In this paper, we introduce an element-free Galerkin (EFG) method based on the moving least-square approximation to approximate positive solutions of the GFE from population dynamics. Compared with other numerical methods, the EFG method for GFE needs only scattered nodes instead of meshing the domain of the problem. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. In comparison with the traditional method, numerical solutions show that the new method has higher accuracy and better convergence. Several numerical examples are presented to demonstrate the effectiveness of the method.

Keywords: element-free Galerkin (EFG) method meshless method generalized Fisher equations (GFE)

Received: 07 November 2012
Revised: 15 December 2012
Accepted manuscript online:

PACS:	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11072117), the Natural Science Foundation of Ningbo City (Grant Nos. 2012A610038 and 2012A610152), the Scientific Research Fund of Education Department of Zhejiang Province, China (Grant No. Z201119278), and K.C. Wong Magna Fund in Ningbo University.

Corresponding Authors: Ge Hong-Xia
E-mail: gehongxia@nbu.edu.cn

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Shi Ting-Yu (时婷玉), Cheng Rong-Jun (程荣军), Ge Hong-Xia (葛红霞) An element-free Galerkin (EFG) method for generalized Fisher equations (GFE) 2013 Chin. Phys. B 22 060210

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An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)

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