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. Baxter, Mathew; Van Gorder, Robert A.: Exact and analytical solutions for a nonlinear sigma model (2014)
  2. Baxter, Mathew; van Gorder, Robert A.; Vajravelu, Kuppalapalle: On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem (2014)
  3. Chan, Leunglung: An exact formula for pricing American exchange options with regime switching (2014)
  4. Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, Shijun: Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel (2014)
  5. Hetmaniok, Edyta; Słota, Damian; Trawiński, Tomasz; Wituła, Roman: Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind (2014)
  6. Huang, Yong; Yuan, Wenjun; Wu, Yonghong: All traveling wave exact solutions of two kinds of nonlinear evolution equations (2014)
  7. Khan, Masood; Shahzad, Azeem; Anjum, Asia; Mahomed, Fazal M.: Analytic approximate solutions for time-dependent flow and heat transfer of a Sisko fluid (2014)
  8. Kumar, Sunil; Rashidi, Mohammad Mehdi: New analytical method for gas dynamics equation arising in shock fronts (2014)
  9. Liang, Songxin; Liu, Sijia: An open problem on the optimality of an asymptotic solution to Duffing’s nonlinear oscillation problem (2014)
  10. Liang, Songxin; Ma, Junchi: Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method (2014)
  11. Liao, Shijun: Do peaked solitary water waves indeed exist? (2014)
  12. Liao, Shijun (ed.): Advances in the homotopy analysis method (2014)
  13. Li, Ronald; van Gorder, Robert A.; Mallory, Kristina; Vajravelu, Kuppalapalle: Solution method for the transformed time-dependent Michaelis-Menten enzymatic reaction model (2014)
  14. Liu, Zeng; Lin, Zhiliang; Liao, Shijun: Phase velocity effects of the wave interaction with exponentially sheared current (2014)
  15. Mallory, Kristina; Van Gorder, Robert A.: Optimal homotopy analysis and control of error for solutions to the non-local Whitham equation (2014)
  16. Mallory, Kristina; Van Gorder, Robert A.: Method for constructing analytical solutions to the Dym initial value problem (2014)
  17. Mastroberardino, Antonio: Comment on “Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink” (2014)
  18. Mastroberardino, Antonio: Mixed convection in viscoelastic boundary layer flow and heat transfer over a stretching sheet (2014)
  19. Motsa, Sandile S.: On the practical use of the spectral homotopy analysis method and local linearisation method for unsteady boundary-layer flows caused by an impulsively stretching plate (2014)
  20. Motsa, S. S.: On an interpolation based spectral homotopy analysis method for PDE based unsteady boundary layer flows (2014)

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