Homotopy analysis method in nonlinear differential equations. ”Homotopy Analysis Method in Nonlinear Differential Equations” presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering.

References in zbMATH (referenced in 204 articles , 1 standard article )

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  1. Motsa, S. S.: On the optimal auxiliary linear operator for the spectral homotopy analysis method solution of nonlinear ordinary differential equations (2014)
  2. Motsa, S. S.: On the bivariate spectral homotopy analysis method approach for solving nonlinear evolution partial differential equations (2014)
  3. Nadeem, S.; Hussain, S. T.: Heat transfer analysis of Williamson fluid over exponentially stretching surface (2014)
  4. Nave, Ophir; Hareli, Shlomo; Gol’dshtein, Vladimir: Singularly perturbed homotopy analysis method (2014)
  5. Panigrahi, S.; Reza, M.; Mishra, A. K.: MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface (2014)
  6. Qian, L. H.; Qian, Y. H.; Chen, S. M.: Homotopy analysis method for homoclinic orbit of a buckled thin plate system (2014)
  7. Zainal, Nor Hafizah; Kılıçman, Adem: Solving fractional partial differential equations with corrected Fourier series method (2014)
  8. Zhao, Yinlong; Liao, Shijun: HAM-based Mathematica package \textttBVPh2.0 for nonlinear boundary value problems (2014)
  9. Abbasbandy, S.; Jalili, M.: Determination of optimal convergence-control parameter value in homotopy analysis method (2013)
  10. Atangana, Abdon; Baleanu, Dumitru: Nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations within Sumudu transform (2013)
  11. Indira, K.; Rajendran, L.: Analytical expressions for the concentrations of substrate, oxygen and mediator in an amperometric enzyme electrode (2013)
  12. Liu, Jincun; Li, Hong: Approximate analytic solutions of time-fractional Hirota-Satsuma coupled KdV equation and coupled MKdV equation (2013)
  13. Liu, Y. P.; Liao, S. J.; Li, Z. B.: Symbolic computation of strongly nonlinear periodic oscillations (2013)
  14. Mallory, Kristina; Van Gorder, Robert A.: Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation (2013)
  15. Nik, H. Saberi; Shateyi, Stanford: Application of optimal HAM for finding feedback control of optimal control problems (2013)
  16. Russo, Matthew; Van Gorder, Robert A.: Control of error in the homotopy analysis of nonlinear Klein-Gordon initial value problems (2013)
  17. Wang, Ping; Cheng, Zunshui: Nonlinear hydroelastic waves beneath a floating ice sheet in a fluid of finite depth (2013)
  18. Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun: An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain (2013)
  19. Duan, Jun-Sheng; Chaolu, Temuer; Rach, Randolph: Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method (2012)
  20. El-Sayed, A. M. A.; Elsaid, A.; Hammad, D.: A reliable treatment of homotopy perturbation method for solving the nonlinear Klein-Gordon equation of arbitrary (fractional) orders (2012)

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