求Riesz空间非线性分数阶对流扩散方程的近似解
Approximate solutions for a Riesz space nonlinear fractional convection-diffusion equation
摘要
在Captuo意义下建立了一类Riesz空间非线性分数阶对流扩散方程,并利用Adomian分解方法给出了该方程满足初始条件的以无穷级数形式表示的解.
This paper establishes a class of a Riesz space nonlinear fractional convection-diffusion equation in the sense of the Captuo.Using Adomian decomposition method,we give the form of infinite series solution of the equation satisfying the initial conditions.
出处
《西南民族大学学报(自然科学版)》
CAS
2010年第6期935-938,共4页
Journal of Southwest Minzu University(Natural Science Edition)
参考文献11
-
1沈淑君,刘发旺.Riesz空间分数阶对流扩散方程的一种计算有效求解方法[J].厦门大学学报(自然科学版),2008,47(1):20-24. 被引量:2
-
2PODLUBNY I.Fractional differential equations[M].San Diego:Academic Press,1999.
-
3SAMKO G,KILBAS A A,MARICHEV O I.Fractional Integrals and Derivatives:Theory and Applications[M].Gordon & Breach,Yverdon,1993.
-
4KEMPLE S,BEYER H.Global and causal solutions of fractional differential equations,in:Transform Methods and Special Functions:Varna96[C].Proceedings of 2nd International Workshop (SCTP),Singapore,1997:210-216.
-
5Shawagfeh N T.The decomposition method for fractional differential equations[J].J Frac Calc,1999,16:27-33.
-
6ADOMIAN G.Solving Frontier Problems of Physics:The Decomposition Method[M].Dordrecht:Kluwer Academic Publishers,1994.
-
7CHERRUALULT Y,ADOMIAN G.Decomposition method:a new proof of convergence[J].Math Comput Modelling,1993,18:103-106.
-
8ABBOUI K,CHERRUAULT Y.New ideas for proving convergence of decomposition methods[J].Comput Math Appl,1995,29 (7):103-105.
-
9CHERRUAULT Y.Convergence of Adomian's method[J].Kybernet-es,1989,18:31-38.
-
10NABIL T.Shawagfeh.Analytical approximate solutions for nonlinear fractional differential equations[M].Math Comput,2002,131:517-529.
二级参考文献18
-
1Ilic M,Liu F,Turner I,et al.Numerical approximation of a fractional-in-space diffusion equation (Ⅱ)-with nonhomogeneous boundary conditions[J].Fractional Calculus & Applied Analysis,2006,9(4):333-349.
-
2Samko S G,Kilbas A A,Marichev O I.Fractional integrals and derivatives:theory and applications[M].Amsterdam:Gordon and Breach,1993.
-
3Podlubny I.Fractional differential equations[M].New York:Academic Press,1999.
-
4Gorenflo R,Mainardi F,Moretti D.Time fractional diffusion:a discrete random walk approach[J].Journal of Nonlinear Dynamics,2000,29:129-143.
-
5Huang F,Liu F.The fundamental solution of the space-time fractional advection-dispersion equation[J].J Appl Math & Computing,2005,18(1/2):339-350.
-
6Meerschaert M M,Scheffler H,Tadjeran C.Finite difference methods for two-dimensional fractional dispersion equation[J].J Comp Phys,2006,211:249-261.
-
7Liu F,Anh V,Turner I.Numerical solution of the space fractional Fokker-Planck equation[J].J Comp Appl Mathematics,2004,166:209-219.
-
8Shen S,Liu F,Anh V,et al.Detailed analysis of an explicit conservative difference approximation for the time fractional diffusion equation[J].J Appl Math Computing,2006,22(3):1-19.
-
9Liu F,Zhuang P,Anh V,et al.Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation[J].Appl Math Comp,2007,191:12-20.
-
10Liu Q,Liu F,Turner I,et al.Approximation of the Lévy-Feller Advection-Dispersion process by random walk and finite difference method[J].Phys Comp,2007,222:57-70.
-
1朱福臣,朱志范,武立中.函数空间φ(L)中某些序收敛性质[J].黑龙江大学自然科学学报,1989,6(3):66-69. 被引量:1
-
2夏莉,黄正洪.三阶发展方程的初边值问题[J].山西大学学报(自然科学版),1998,21(1):10-15.
-
3夏莉,邓学清.一类三阶发展方程的初边值问题的近似解[J].西南师范大学学报(自然科学版),1997,22(2):214-219.
-
4陈芳.Riesz空间中序收敛的几点注记[J].长江大学学报(自科版)(上旬),2013,10(3):6-7.
-
5何桃顺,陈滋利.Archimedean-Riesz空间中的带算子(英文)[J].四川师范大学学报(自然科学版),2012,35(4):510-514.
-
6李孜,倪晋龙.一类Volterra捕食者-食饵模型的解析解[J].通化师范学院学报,2009,30(4):5-6.
-
7崔光云.一类拟线性方程的奇异边值问题[J].河南师范大学学报(自然科学版),1997,25(2):21-24.
-
8郭瑞,赵西卿,张利霞,许宏鑫.关于欧拉方程φ(mn)=2×3(φ(m)+φ(n))的正整数解[J].贵州师范大学学报(自然科学版),2016,34(2):60-63. 被引量:16
-
9蓝爱群.物理中的矩阵及应用[J].科学时代,2009(2):168-169.
-
10金贵荣.用积分形式表示幂级数∝∑n=1x^n/n^k(k≥2)[J].庆阳师专学报(自然科学版),1994(2):9-12.