AAM  >> Vol. 6 No. 4 (July 2017)

    地下水流区域上的异质含水层模型的分段Adomian近似解
    Segmented Adomian Approximate Solution of Heterogeneous Aquifer Model of Groundwater Flow

  • 全文下载: PDF(431KB) HTML   XML   PP.435-441   DOI: 10.12677/AAM.2017.64051  
  • 下载量: 1,067  浏览量: 1,618  

作者:  

温颖,银山:内蒙古工业大学理学院,内蒙古 呼和浩特

关键词:
分段Adomian算法偏微分方程地下水流区域上的异质含水层模型Segmented Adomian Algorithm Partial Differential Equation Modeling of the Heterogeneous Aquifer

摘要:

基于Adomian分解法和Taylor公式,给出三角形地下水流区域上的异质含水层模型的分段Adomian近似解。为三角形区域对应的二阶偏微分方程的边值问题提供一个新的Adomain算法。

Based on the Adomian decomposition method and the Taylor formula,a segmented Adomian approximate solution of the heterogeneous aquifer model on the triangular groundwater flow region is provided. A new Adomain algorithm is provided for (initial) boundary value problem of the second order partial differential equation on the triangular region. 

文章引用:
温颖, 银山. 地下水流区域上的异质含水层模型的分段Adomian近似解[J]. 应用数学进展, 2017, 6(4): 435-441. https://doi.org/10.12677/AAM.2017.64051

参考文献

[1] Bluman, G.W. and Kumei, S. (1989) Symmetries and Differential Equations. Springer-Verlag, New York.
https://doi.org/10.1007/978-1-4757-4307-4
[2] Yun, Y.S. and Temuer, C.L. (2015) Classical and Nonclassical Symmetry Classifications of Nonlinear Wave Equation with Dissipation. Applied Mathematics and Mechanics (English Edition), 36, 365-378.
https://doi.org/10.1007/s10483-015-1910-6
[3] Adomian, G. (1988) A Review of the Decomposition Method in Applied Mathematics. Journal of Mathematical Analysis and Applications, 135, 501-544.
https://doi.org/10.1016/0022-247X(88)90170-9
[4] He, J.H. (2000) A Coupling Method of a Homotopy Technique and a Perturbation Technique for Non-Linear Problems. International Journal of Non-Linear Mechanics, 35, 37-43.
https://doi.org/10.1016/S0020-7462(98)00085-7
[5] Yun, Y.S. and Temuer, C.L. (2015) Application of the Homotopy Perturbation Method for the Large Deflection Problem of a Circular Plate. Applied Mathematical Modelling, 39, 1308-1316.
https://doi.org/10.1016/j.apm.2014.09.001
[6] Liao, S.J. (1992) The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems. Ph.D. Thesis, Shanghai Jiao Tong University, Shang Hai.
[7] Fan, E.G. (2000) Extended Tanh-Function Method and Its Applications to Nonlinear Equations. Physics Letters A, 277, 212-220.
https://doi.org/10.1016/S0375-9601(00)00725-8
[8] Yun, Y.S. and Temuer, C.L. (2011) A Further Improved Tanh Method and New Traveling Wave Solutions of 2D-KdV Equation. Journal of Inner Mongolia University (Natural Science Edition), 42, 604-609.
[9] Duan, J.S. (2010) Recurrence Triangle for Adomian Polynomials. Applied Mathematics and Computation, 216, 1235-1241.
https://doi.org/10.1016/j.amc.2010.02.015
[10] Duan, J.S. (2011) Convenient Analytic Recurrence Algorithms for the Adomian Polynomials. Applied Mathematics and Computation, 217, 6337-6348.
https://doi.org/10.1016/j.amc.2011.01.007
[11] Cherruault, Y. (1989) Convergence of Adomian’s Method. Kybernetes, 18, 31-38.
https://doi.org/10.1108/eb005812
[12] Wazwaz, A.M. (2002) A New Method for Solving Singular Initial Value Problem in the Second-Order Ordinary Differential Equations. Applied Mathematics and Computation, 128, 45-57.
[13] Lesnic, D. (2006) Blow-Up Solutions Obtained Using the Decompotion Method. Chaos, Solution & Fractals, 28, 776- 787.
[14] 朱永贵, 朝鲁. Adomian分解法在求解微分方程定解问题中的应用[J]. 内蒙古大学学报(自然科学版), 2004, 35(4): 381-385.
[15] Shidfar, A. and Garshasbi, M. (2009) A Weighted Algorithm Based on Adomian Decomposition Method for Solving a Special Class of Evolution Equations. Communications in Nonlinear Science and Numerical Simulation, 14, 1146- 1151.
[16] Patel, A. and Serrano, S.E. (2011) Decomposition Solution of Multidimensional Groundwater Equations. Journal of Hydrology, 397, 202-209.
[17] Yun, Y.S. Temuer, C.L. and Duan, J.S. (2014) A Segmented and Weighted Adomian Decomposition Algorithm for Boundary Value Problem of Nonlinear Groundwater Equation. Mathematical Methods in the Applied Sciences, 37, 2406-2418.
https://doi.org/10.1002/mma.2986