中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60210-060210.doi: 10.1088/1674-1056/22/6/060210
时婷玉a, 程荣军b, 葛红霞a
Shi Ting-Yu (时婷玉)a, Cheng Rong-Jun (程荣军)b, Ge Hong-Xia (葛红霞)a
摘要: 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.
中图分类号: (Ordinary and partial differential equations; boundary value problems)