时-空分数阶扩散方程的同伦近似解  

Approximate Solutions of Time-Space Fractional Diffusion Equation By Homotopy Analysis Method

作　　者：谭璐芸[1] 

机构地区：[1]铁岭师范高等专科学校师范学院,辽宁铁岭112000

出　　处：《延安大学学报（自然科学版）》2014年第2期6-9,共4页Journal of Yan'an University：Natural Science Edition

摘　　要：利用同伦分析方法,研究了具有初值条件的空间二维时空分数阶扩散方程。从问题本身考虑,通过构造同伦方程,合理选择辅助参数,获得了在较大范围内收敛的级数解析解。数值实验结果证明,该法在求解分数阶偏微分方程的近似解析解方面的有效性和优越性。The homotopy analysis method is applied to study the two - dimensional time - space fractional diffusion equation with initial conditions. By constructing homotopy equation and by a reasonable choice of auxiliary parameters, the analytical solutions of a wide range of convergent series are obtained. Numerical results show that this method is effective and superior in solving partial differential equations of fractional.

关 键 词：分数阶偏微分方程 同伦分析方法 近似解 

分 类 号：O175.29[理学—数学]