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Volumn 16, Issue 11, 2011, Pages 4268-4275

Mathematical properties of ℏ-curve in the frame work of the homotopy analysis method

Author keywords

Convergence controller parameter; Homotopy analysis method; Horizontal line; Curve

Indexed keywords

ANALYSIS METHOD; CONTROL PARAMETERS; CONTROLLER PARAMETER; CONVERGENCE-CONTROLLER PARAMETER; FRAME-WORK; HOMOTOPY ANALYSE METHOD; HOMOTOPY ANALYSIS; HORIZONTAL LINE; PROPERTY; ℏ-CURVE;

EID: 79957919455     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.03.031     Document Type: Article
Times cited : (127)

References (57)
  • 1
    • 85196213553 scopus 로고
    • The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D thesis, Shanghai Jiao Tong University, Shanghai;
    • Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D thesis, Shanghai Jiao Tong University, Shanghai; 1992.
    • (1992)
    • Liao, S.J.1
  • 2
    • 76049117931 scopus 로고    scopus 로고
    • An optimal homotopy-analysis approach for strongly nonlinear differential equations
    • Liao S.J. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun Nonlinear Sci Numer Simulat 2010, 15:2003-2016.
    • (2010) Commun Nonlinear Sci Numer Simulat , vol.15 , pp. 2003-2016
    • Liao, S.J.1
  • 3
    • 0031232480 scopus 로고    scopus 로고
    • A kind of approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics
    • Liao S.J. A kind of approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics. Int J Non-Linear Mech 1997, 32:815-822.
    • (1997) Int J Non-Linear Mech , vol.32 , pp. 815-822
    • Liao, S.J.1
  • 5
    • 55549136027 scopus 로고    scopus 로고
    • Notes on the homotopy analysis method: some definitions and theorems
    • Liao S.J. Notes on the homotopy analysis method: some definitions and theorems. Commun Nonlinear Sci Numer Simulat 2009, 14:983-997.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 983-997
    • Liao, S.J.1
  • 6
    • 34347219047 scopus 로고    scopus 로고
    • Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid
    • Hayat T., Javed T., Sajid M. Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid. Acta Mech 2007, 191:219-229.
    • (2007) Acta Mech , vol.191 , pp. 219-229
    • Hayat, T.1    Javed, T.2    Sajid, M.3
  • 7
    • 34248519246 scopus 로고    scopus 로고
    • Rotating flow of a third-grade fluid in a porous space with hall current
    • Hayat T., Khan M., SajidM M., Asghar S. Rotating flow of a third-grade fluid in a porous space with hall current. Nonlinear Dyn 2007, 49:83-91.
    • (2007) Nonlinear Dyn , vol.49 , pp. 83-91
    • Hayat, T.1    Khan, M.2    SajidM, M.3    Asghar, S.4
  • 8
    • 33845432502 scopus 로고    scopus 로고
    • On analytic solution for thin film flow of a forth grade fluid down a vertical cylinder
    • Hayat T., Sajid M. On analytic solution for thin film flow of a forth grade fluid down a vertical cylinder. Phys Lett A 2007, 361:316-322.
    • (2007) Phys Lett A , vol.361 , pp. 316-322
    • Hayat, T.1    Sajid, M.2
  • 9
    • 33750714429 scopus 로고    scopus 로고
    • Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet
    • Hayat T., Sajid M. Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet. Int J Heat Mass Transf 2007, 50:75-84.
    • (2007) Int J Heat Mass Transf , vol.50 , pp. 75-84
    • Hayat, T.1    Sajid, M.2
  • 10
    • 33846635947 scopus 로고    scopus 로고
    • The influence of thermal radiation on MHD flow of a second grade fluid
    • Hayat T., Abbas Z., Sajid M., Asghar S. The influence of thermal radiation on MHD flow of a second grade fluid. Int J Heat Mass Transf 2007, 50:931-941.
    • (2007) Int J Heat Mass Transf , vol.50 , pp. 931-941
    • Hayat, T.1    Abbas, Z.2    Sajid, M.3    Asghar, S.4
  • 11
    • 34447642165 scopus 로고    scopus 로고
    • Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid
    • Hayat T., Sajid M. Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid. Int J Eng Sci 2007, 45:393-401.
    • (2007) Int J Eng Sci , vol.45 , pp. 393-401
    • Hayat, T.1    Sajid, M.2
  • 12
    • 34250841231 scopus 로고    scopus 로고
    • On the MHD flow of a second grade fluid in a porous channel
    • Hayat T., Ahmed N., Sajid M., Asghar S. On the MHD flow of a second grade fluid in a porous channel. Comput Math Appl 2007, 54:14-40.
    • (2007) Comput Math Appl , vol.54 , pp. 14-40
    • Hayat, T.1    Ahmed, N.2    Sajid, M.3    Asghar, S.4
  • 13
    • 33847032526 scopus 로고    scopus 로고
    • The effect of the slip condition on flows of an Oldroyd 6 constant fluid
    • Hayat T., Khan M., Ayub M. The effect of the slip condition on flows of an Oldroyd 6 constant fluid. J Comput Appl 2007, 202:402-413.
    • (2007) J Comput Appl , vol.202 , pp. 402-413
    • Hayat, T.1    Khan, M.2    Ayub, M.3
  • 14
    • 34447622123 scopus 로고    scopus 로고
    • Wire coating analysis using MHD Oldroyd 8-constant fluid
    • Sajid M., Siddiqui A., Hayat T. Wire coating analysis using MHD Oldroyd 8-constant fluid. Int J Eng Sci 2007, 45:381-392.
    • (2007) Int J Eng Sci , vol.45 , pp. 381-392
    • Sajid, M.1    Siddiqui, A.2    Hayat, T.3
  • 15
    • 33847224443 scopus 로고    scopus 로고
    • Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet
    • Sajid M., Hayat T., Asghar S. Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet. Int J Heat Mass Transf 2007, 50:1723-1736.
    • (2007) Int J Heat Mass Transf , vol.50 , pp. 1723-1736
    • Sajid, M.1    Hayat, T.2    Asghar, S.3
  • 16
    • 33947616288 scopus 로고    scopus 로고
    • Non-similar solution for the axisymmetric flow of a third-grade fluid over radially stretching sheet
    • Sajid M., Hayat T., Asghar S. Non-similar solution for the axisymmetric flow of a third-grade fluid over radially stretching sheet. Acta Mech 2007, 189:193-205.
    • (2007) Acta Mech , vol.189 , pp. 193-205
    • Sajid, M.1    Hayat, T.2    Asghar, S.3
  • 17
    • 35448933724 scopus 로고    scopus 로고
    • Soliton solutions for the 5th-order KdV equation with the homotopy analysis method
    • Abbasbandy S. Soliton solutions for the 5th-order KdV equation with the homotopy analysis method. Nonlinear Dyn 2008, 51:83-87.
    • (2008) Nonlinear Dyn , vol.51 , pp. 83-87
    • Abbasbandy, S.1
  • 18
    • 33845907123 scopus 로고    scopus 로고
    • The application of the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation
    • Abbasbandy S. The application of the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Phys Lett A 2007, 361:478-483.
    • (2007) Phys Lett A , vol.361 , pp. 478-483
    • Abbasbandy, S.1
  • 19
    • 34347339334 scopus 로고    scopus 로고
    • Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation
    • Song L., Zhang H.Q. Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation. Phys Lett A 2007, 367:88-94.
    • (2007) Phys Lett A , vol.367 , pp. 88-94
    • Song, L.1    Zhang, H.Q.2
  • 20
    • 41449097382 scopus 로고    scopus 로고
    • Series solutions of nano boundary layer flows by means of the homotopy analysis method
    • Cheng J., Liao S.J., Mohapatra R.N., Vajravelu K. Series solutions of nano boundary layer flows by means of the homotopy analysis method. J Math Anal Appl 2008, 343:233-245.
    • (2008) J Math Anal Appl , vol.343 , pp. 233-245
    • Cheng, J.1    Liao, S.J.2    Mohapatra, R.N.3    Vajravelu, K.4
  • 21
    • 33750339270 scopus 로고    scopus 로고
    • The application of the homotopy analysis method to nonlinear equations arising in heat transfer
    • Abbasbandy S. The application of the homotopy analysis method to nonlinear equations arising in heat transfer. Phys Lett A 2006, 360:109-113.
    • (2006) Phys Lett A , vol.360 , pp. 109-113
    • Abbasbandy, S.1
  • 22
    • 33847658380 scopus 로고    scopus 로고
    • Homotopy analysis method for heat radiation equations
    • Abbasbandy S. Homotopy analysis method for heat radiation equations. Int Commun Heat Mass Transf 2007, 34:380-387.
    • (2007) Int Commun Heat Mass Transf , vol.34 , pp. 380-387
    • Abbasbandy, S.1
  • 23
    • 33744970924 scopus 로고    scopus 로고
    • An exact and explicit solution for the valuation of American put options
    • Zhu S.P. An exact and explicit solution for the valuation of American put options. Quant Fin 2006, 6:229-242.
    • (2006) Quant Fin , vol.6 , pp. 229-242
    • Zhu, S.P.1
  • 24
    • 33748467284 scopus 로고    scopus 로고
    • A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield
    • Zhu S.P. A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield. Anziam J 2006, 47:477-494.
    • (2006) Anziam J , vol.47 , pp. 477-494
    • Zhu, S.P.1
  • 25
    • 48749083737 scopus 로고    scopus 로고
    • Explicit solution to the exact Riemann problem and application in nonlinear shallow-water equations
    • Wu Y., Cheung K.F. Explicit solution to the exact Riemann problem and application in nonlinear shallow-water equations. Int J Numer Meth Fluids 2008, 57:1649-1668.
    • (2008) Int J Numer Meth Fluids , vol.57 , pp. 1649-1668
    • Wu, Y.1    Cheung, K.F.2
  • 26
    • 34547420243 scopus 로고    scopus 로고
    • An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method
    • Yamashita M., Yabushita K., Tsuboi K. An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method. J Phys A 2007, 40:8403-8416.
    • (2007) J Phys A , vol.40 , pp. 8403-8416
    • Yamashita, M.1    Yabushita, K.2    Tsuboi, K.3
  • 27
    • 33845601283 scopus 로고    scopus 로고
    • Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method
    • Bouremel Y. Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method. Commun Nonlinear Sci Numer Simulat 2007, 12(5):714-724.
    • (2007) Commun Nonlinear Sci Numer Simulat , vol.12 , Issue.5 , pp. 714-724
    • Bouremel, Y.1
  • 28
    • 35348955411 scopus 로고    scopus 로고
    • Nonlinear progressive waves in water of finite depth-an analytic approximation
    • Tao L., Song H., Chakrabarti S. Nonlinear progressive waves in water of finite depth-an analytic approximation. Clastal Eng 2007, 54:825-834.
    • (2007) Clastal Eng , vol.54 , pp. 825-834
    • Tao, L.1    Song, H.2    Chakrabarti, S.3
  • 29
    • 41449101099 scopus 로고    scopus 로고
    • Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media
    • Song H., Tao L. Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media. J Coastal Res 2007, 50:292-295.
    • (2007) J Coastal Res , vol.50 , pp. 292-295
    • Song, H.1    Tao, L.2
  • 30
    • 56549119386 scopus 로고    scopus 로고
    • The homotopy analysis method to solve the Burgers-Huxley equation
    • Molabahrami A., Khani F. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Anal B: Real World Appl 2009, 10:589-600.
    • (2009) Nonlinear Anal B: Real World Appl , vol.10 , pp. 589-600
    • Molabahrami, A.1    Khani, F.2
  • 31
    • 35348973440 scopus 로고    scopus 로고
    • Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method
    • Bataineh A.S., Noorani M.S.M., Hashim I. Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method. Phys Lett A 2007, 371:72-82.
    • (2007) Phys Lett A , vol.371 , pp. 72-82
    • Bataineh, A.S.1    Noorani, M.S.M.2    Hashim, I.3
  • 32
    • 34548203117 scopus 로고    scopus 로고
    • Applying homotopy analysis method for solving differential-difference equation
    • Wang Z., Zou L., Zhang H. Applying homotopy analysis method for solving differential-difference equation. Phys Lett A 2007, 369:77-84.
    • (2007) Phys Lett A , vol.369 , pp. 77-84
    • Wang, Z.1    Zou, L.2    Zhang, H.3
  • 33
    • 34247352920 scopus 로고    scopus 로고
    • On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method
    • Inc M. On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method. Phys Lett A 2007, 365:412-415.
    • (2007) Phys Lett A , vol.365 , pp. 412-415
    • Inc, M.1
  • 34
    • 85196205563 scopus 로고    scopus 로고
    • Nonlinear dynamics of thermal-hydraulic networks. Ph.D. thesis, University of Notre Dame;
    • Cai WH. Nonlinear dynamics of thermal-hydraulic networks. Ph.D. thesis, University of Notre Dame; 2006.
    • (2006)
    • Cai, W.H.1
  • 35
    • 41649091786 scopus 로고    scopus 로고
    • The application of homotopy analysis method for 2-dimensional steady slip flow in microchannels
    • Zhang T.T., Jia L., Wang Z.C., Li X. The application of homotopy analysis method for 2-dimensional steady slip flow in microchannels. Phys Lett A 2008, 372:3223-3227.
    • (2008) Phys Lett A , vol.372 , pp. 3223-3227
    • Zhang, T.T.1    Jia, L.2    Wang, Z.C.3    Li, X.4
  • 36
    • 56049110221 scopus 로고    scopus 로고
    • Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system
    • Alomari A.K., Noorani M.S.M., Nazar R. Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system. Commun Nonlinear Sci Numer Simul 2009, 4:2336-2346.
    • (2009) Commun Nonlinear Sci Numer Simul , vol.4 , pp. 2336-2346
    • Alomari, A.K.1    Noorani, M.S.M.2    Nazar, R.3
  • 37
    • 42949165898 scopus 로고    scopus 로고
    • The application of homotopy analysis method to thin film flows of a third order fluid
    • Sajid M., Hayat T. The application of homotopy analysis method to thin film flows of a third order fluid. Chaos Solitons Fract 2008, 38:506-515.
    • (2008) Chaos Solitons Fract , vol.38 , pp. 506-515
    • Sajid, M.1    Hayat, T.2
  • 38
    • 35348973440 scopus 로고    scopus 로고
    • Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method
    • Bataineh A.S., Noorani M.S.M., Hashim I. Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method. Phys Lett A 2007, 371:72-82.
    • (2007) Phys Lett A , vol.371 , pp. 72-82
    • Bataineh, A.S.1    Noorani, M.S.M.2    Hashim, I.3
  • 39
    • 38949143275 scopus 로고    scopus 로고
    • Analytic solution for flow of Sisko fluid through a porous medium Authors
    • Khan M., Abbas Z., Hayat T. Analytic solution for flow of Sisko fluid through a porous medium Authors. Trans Porous Media 2008, 71:23-37.
    • (2008) Trans Porous Media , vol.71 , pp. 23-37
    • Khan, M.1    Abbas, Z.2    Hayat, T.3
  • 40
    • 50349103358 scopus 로고    scopus 로고
    • Analytic and numerical solutions to the Lane-Emden equation
    • A Van Gorder R., Vajravelu K. Analytic and numerical solutions to the Lane-Emden equation. Phys Lett A 2008, 372:6060-6065.
    • (2008) Phys Lett A , vol.372 , pp. 6060-6065
    • A Van Gorder, R.1    Vajravelu, K.2
  • 41
    • 67349169966 scopus 로고    scopus 로고
    • On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach
    • Van Gorder R.A., Vajravelu K. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach. Commun Nonlinear Sci Numer Simul 2009, 14:4078-4089.
    • (2009) Commun Nonlinear Sci Numer Simul , vol.14 , pp. 4078-4089
    • Van Gorder, R.A.1    Vajravelu, K.2
  • 42
    • 56049098395 scopus 로고    scopus 로고
    • Investigation of a powerful analytical method into natural convection boundary layer flow
    • Ghotbi A.R., Bararnia, Domairry G., Barari A. Investigation of a powerful analytical method into natural convection boundary layer flow. Commun Nonlinear Sci Numer Simulat 2009, 14:2222-2228.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 2222-2228
    • Ghotbi, A.R.1    Bararnia Domairry, G.2    Barari, A.3
  • 43
    • 71949102019 scopus 로고    scopus 로고
    • Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet
    • Ayub M., Zaman H., Ahmad M. Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet. Cent Eur J Phys 2010, 8:135-149.
    • (2010) Cent Eur J Phys , vol.8 , pp. 135-149
    • Ayub, M.1    Zaman, H.2    Ahmad, M.3
  • 44
    • 33747865377 scopus 로고    scopus 로고
    • Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones
    • Liao S.J., Magyari E. Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. J Appl Math Phys 2006, 57:777-792.
    • (2006) J Appl Math Phys , vol.57 , pp. 777-792
    • Liao, S.J.1    Magyari, E.2
  • 45
    • 34547506935 scopus 로고    scopus 로고
    • A new branch of solutions of boundary-layer flows over a permeable stretching plate
    • Liao S.J. A new branch of solutions of boundary-layer flows over a permeable stretching plate. Int J Non-Linear Mech 2007, 42:819-830.
    • (2007) Int J Non-Linear Mech , vol.42 , pp. 819-830
    • Liao, S.J.1
  • 46
    • 34548067424 scopus 로고    scopus 로고
    • Dual solutions of boundary layer flow over an upstream moving plate
    • Xu H., Liao S.J. Dual solutions of boundary layer flow over an upstream moving plate. Commun Nonlinear Sci Numer Simulat 2008, 13:350-358.
    • (2008) Commun Nonlinear Sci Numer Simulat , vol.13 , pp. 350-358
    • Xu, H.1    Liao, S.J.2
  • 47
    • 25844478165 scopus 로고    scopus 로고
    • An analytic approach to solve multiple solutions of a strongly nonlinear problem
    • Li S., Liao S.J. An analytic approach to solve multiple solutions of a strongly nonlinear problem. Appl Math Comput 2005, 169:854-865.
    • (2005) Appl Math Comput , vol.169 , pp. 854-865
    • Li, S.1    Liao, S.J.2
  • 48
    • 77954496246 scopus 로고    scopus 로고
    • Homotopy based solutions of the Navier-stokes equations for a porous channel with orthogonally moving walls
    • Xu H., Lin Z.L., Liao S.J., Wu J.Z., Majdalani J. Homotopy based solutions of the Navier-stokes equations for a porous channel with orthogonally moving walls. Phys Fluids 2010, 22:053601.
    • (2010) Phys Fluids , vol.22 , pp. 053601
    • Xu, H.1    Lin, Z.L.2    Liao, S.J.3    Wu, J.Z.4    Majdalani, J.5
  • 49
    • 77950866758 scopus 로고    scopus 로고
    • The essence of the generalized Newton binomial theorem
    • Liu C.S. The essence of the generalized Newton binomial theorem. Commun Nonlinear Sci Numer Simul 2010, 15:2766-2768.
    • (2010) Commun Nonlinear Sci Numer Simul , vol.15 , pp. 2766-2768
    • Liu, C.S.1
  • 50
    • 77949917814 scopus 로고    scopus 로고
    • The essence of the homotopy analysis method
    • Liu C.S. The essence of the homotopy analysis method. Appl Math Comput 2010, 216:1299-1303.
    • (2010) Appl Math Comput , vol.216 , pp. 1299-1303
    • Liu, C.S.1
  • 51
    • 77953938224 scopus 로고    scopus 로고
    • Comparison of a general series expansion method and the homotopy analysis method
    • Liu C.S., Liu Y. Comparison of a general series expansion method and the homotopy analysis method. Mod Phys Lett B 2010, 24:1699-1706.
    • (2010) Mod Phys Lett B , vol.24 , pp. 1699-1706
    • Liu, C.S.1    Liu, Y.2
  • 52
    • 77957333487 scopus 로고    scopus 로고
    • The essence of the generalized Taylor theorem as the foundation of the homotopy analysis method
    • Liu C.S. The essence of the generalized Taylor theorem as the foundation of the homotopy analysis method. Commun Nonlinear Sci Numer Simul 2011, 16:1254-1262.
    • (2011) Commun Nonlinear Sci Numer Simul , vol.16 , pp. 1254-1262
    • Liu, C.S.1
  • 53
    • 77955658683 scopus 로고    scopus 로고
    • A study on the convergence of homotopy analysis method
    • Odibat Z. A study on the convergence of homotopy analysis method. Appl Math Comput 2010, 217:782789.
    • (2010) Appl Math Comput , vol.217 , pp. 782789
    • Odibat, Z.1
  • 54
    • 63449128519 scopus 로고    scopus 로고
    • The homotopy analysis method for multiple solutions of nonlinear boundary value problems
    • Abbasbandy S., Magyari E., Shivanian E. The homotopy analysis method for multiple solutions of nonlinear boundary value problems. Commun Nonlinear Sci Numer Simulat 2009, 14:3530-3536.
    • (2009) Commun Nonlinear Sci Numer Simulat , vol.14 , pp. 3530-3536
    • Abbasbandy, S.1    Magyari, E.2    Shivanian, E.3
  • 55
    • 77952746263 scopus 로고    scopus 로고
    • Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method
    • Abbasbandy S., Shivanian E. Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method. Commun Nonlinear Sci Numer Simulat 2010, 15:3830-3846.
    • (2010) Commun Nonlinear Sci Numer Simulat , vol.15 , pp. 3830-3846
    • Abbasbandy, S.1    Shivanian, E.2
  • 56
    • 78651458045 scopus 로고    scopus 로고
    • Predictor homotopy analysis method and its application to some nonlinear problems
    • Abbasbandy S., Shivanian E. Predictor homotopy analysis method and its application to some nonlinear problems. Commun Nonlinear Sci Numer Simulat 2011, 16:2456-2468.
    • (2011) Commun Nonlinear Sci Numer Simulat , vol.16 , pp. 2456-2468
    • Abbasbandy, S.1    Shivanian, E.2


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