S. Abbasbandy, LIAO Shi-jun. A New Modification of False Position Method Based on the Homotopy Analysis Method[J]. Applied Mathematics and Mechanics, 2008, 29(2): 203-208.
Citation: S. Abbasbandy, LIAO Shi-jun. A New Modification of False Position Method Based on the Homotopy Analysis Method[J]. Applied Mathematics and Mechanics, 2008, 29(2): 203-208.

A New Modification of False Position Method Based on the Homotopy Analysis Method

  • Received Date: 2007-08-16
  • Rev Recd Date: 2008-01-14
  • Publish Date: 2008-02-15
  • A new modification of false position method for solving nonlinear equations is presented by applying homotopy analysis method(HAM).Some numerical illustrations are given to show the efficiency of algorithm.
  • loading
  • [1]
    Burden R L,Faires J D.Numerical Analysis[M].7th Ed.Pacific Grove,California:Brooks/Cole, 2000.
    [2]
    Wu T M.A modified formula of ancient Chinese algorithm by the homotopy continuation technique[J].Appl Math Comput,2005,165(1):31-35. doi: 10.1016/j.amc.2004.04.114
    [3]
    LIAO Shi-jun.The proposed homotopy analysis technique for the solution of nonlinear problems[D].Ph D Thesis.Shanghai:Shanghai Jiaotong University,1992.
    [4]
    Liao S J. An approximate solution technique which does not depend upon small parameters:a special example[J].International Journal of Nonlinear Mechanics,1995,30(3):371-380. doi: 10.1016/0020-7462(94)00054-E
    [5]
    Liao S J. An approximate solution technique which does not depend upon small parameters (Part 2):an application in fluid mechanics[J].International Journal of Non-Linear Mechanics,1997,32(5):815-822. doi: 10.1016/S0020-7462(96)00101-1
    [6]
    Liao S J.An explicit,totally analytic approximation of Blasius viscous flow problems[J].International Journal of Non-Linear Mechanics,1999,34(4):759-778. doi: 10.1016/S0020-7462(98)00056-0
    [7]
    Liao S J.Beyond Perturbation. Introduction to the Homotopy Analysis Method[M].Boca Raton:Chapman & Hall/CRC Press,2003.
    [8]
    Liao S J. On the homotopy anaylsis method for nonlinear problems[J].Appl Math Comput,2004,147(2):499-513. doi: 10.1016/S0096-3003(02)00790-7
    [9]
    Liao S J. Comparison between the homotopy analysis method and homotopy perturbation method[J].Appl Math Comput,2005,169(2):1186-1194. doi: 10.1016/j.amc.2004.10.058
    [10]
    Ayub M, Rasheed A,Hayat T.Exact flow of a third grade fluid past a porous plate using homotopy analysis method[J].Internat J Engng Sci,2003,41(18):2091-2103. doi: 10.1016/S0020-7225(03)00207-6
    [11]
    Hayat T, Khan M,Ayub M.On the explicit analytic solutions of an Oldroyd 6-constant fluid[J].Internat J Engng Sci,2004,42(2):123-135. doi: 10.1016/S0020-7225(03)00281-7
    [12]
    Liao S J.A new branch of solutions of boundary-layer flows over an impermeable stretched plate[J].Internat J Heat Mass Transfer,2005,48(12):2529-2539. doi: 10.1016/j.ijheatmasstransfer.2005.01.005
    [13]
    Liao S J, Pop I.Explicit analytic solution for similarity boundary layer equations[J].Internat J Heat Mass Transfer,2004,47(1):75-85. doi: 10.1016/S0017-9310(03)00405-8
    [14]
    Abbasbandy S.Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method[J].Appl Math Comput,2003,145(2/3):887-893. doi: 10.1016/S0096-3003(03)00282-0
    [15]
    Abbasbandy S.Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method[J].Appl Math Comput,2006,172(1):431-438. doi: 10.1016/j.amc.2005.02.015
    [16]
    Liao S J. An explicit analytic solution to the Thomas-Fermi equation[J].Appl Math Comput,2003,144(2/3):495-506. doi: 10.1016/S0096-3003(02)00423-X
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2680) PDF downloads(605) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return