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A new modification of false position method based on homotopy analysis method. (English) Zbl 1231.65084
Summary: 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.

MSC:
65H05 Numerical computation of solutions to single equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
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[1] Burden R L, Faires J D. Numerical analysis[M]. 7th Edition, Brooks/Cole, 2000.
[2] Wu T M. A modified formula of ancient Chinese algorithm by the homotopy continuation technique[J]. Appl Math Comput, 2005, 165:31–35. · Zbl 1070.65035 · doi:10.1016/j.amc.2004.04.114
[3] Liao S J. The proposed homotopy analysis technique for the solution of nonlinear problems[D]. Ph D Dissertation. 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 Non-linear Mechanics, 1995, 30:371–380. · Zbl 0837.76073 · 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. · Zbl 1031.76542 · 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. · Zbl 1342.74180 · 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, 147:499–513. · Zbl 1086.35005 · 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, 169:1186–1194. · Zbl 1082.65534 · 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]. Int J Eng Sci, 2003, 41:2091–2103. · Zbl 1211.76076 · 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]. Int J Eng Sci, 2004, 42:123–135. · Zbl 1211.76009 · 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]. Int J Heat Mass Transfer, 2005, 48:2529–2539. · Zbl 1189.76142 · doi:10.1016/j.ijheatmasstransfer.2005.01.005
[13] Liao S J, Pop I. Explicit analytic solution for similarity boundary layer equations[J]. Int J Heat Mass Transfer, 2004, 47:75–78. · Zbl 1045.76008 · 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, 145:887–893. · Zbl 1032.65048 · 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, 172:431–438. · Zbl 1088.65043 · 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, 144:433–444. · Zbl 1034.34005 · doi:10.1016/S0096-3003(02)00423-X
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