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 100 articles , 1 standard article )

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  1. Baxter, Mathew; Dewasurendra, Mangalagama; Vajravelu, Kuppalapalle: A method of directly defining the inverse mapping for solutions of coupled systems of nonlinear differential equations (2018)
  2. Cui, Jifeng; Zhang, Wenyu; Liu, Zeng; Sun, Jianglong: On the limit cycles, period-doubling, and quasi-periodic solutions of the forced van der Pol-Duffing oscillator (2018)
  3. Fu, H. X.; Qian, Y. H.: Study on a multi-frequency homotopy analysis method for period-doubling solutions of nonlinear systems (2018)
  4. Nave, Ophir; Elbaz, Miriam: Method of directly defining the inverse mapping applied to prostate cancer immunotherapy -- mathematical model (2018)
  5. Saberi Najafi, H.; Edalatpanah, S. A.; Refahisheikhani, A. H.: An analytical method as a preconditioning modeling for systems of linear equations (2018)
  6. Yang, Xiaoyan; Dias, Frederic; Liao, Shijun: On the steady-state resonant acoustic-gravity waves (2018)
  7. Yang, Zhaochen; Liao, Shijun: On the generalized wavelet-Galerkin method (2018)
  8. Hayat, T.; Kiran, A.; Imtiaz, M.; Alsaedi, A.: Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid (2017)
  9. Jaradat, Ali; Awawdeh, Fadi; Noorani, Mohd Salmi Md: Identification of time-dependent source terms and control parameters in parabolic equations from overspecified boundary data (2017)
  10. Najafi, Ramin; Küçük, Gökçe Dilek; Çelik, Ercan: Modified iteration method for solving fractional gas dynamics equation (2017)
  11. Ouyang, Cheng; Zhu, Min; Mo, Jiaqi: A class of epidemic virus transmission population dynamic system (2017)
  12. Pandey, Rishi Kumar; Mishra, Hradyesh Kumar: Homotopy analysis Sumudu transform method for time -- fractional third order dispersive partial differential equation (2017)
  13. Shehzad, S. A.; Hayat, T.; Alsaedi, A.; Meraj, M. A.: Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid (2017)
  14. Van Gorder, Robert A.: On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations (2017)
  15. Zhang, Xiaolong; Liang, Songxin; Zou, Li: Uniqueness and error estimates for solutions to higher-order boundary value problems (2017)
  16. Zhong, Xiaoxu; Liao, Shijun: On the homotopy analysis method for backward/forward-backward stochastic differential equations (2017)
  17. Zhong, X. X.; Liao, S. J.: Analytic solutions of Von Kármán plate under arbitrary uniform pressure -- equations in differential form (2017)
  18. Alsaedi, A.; Hayat, T.; Muhammad, T.; Shehzad, S. A.: MHD three-dimensional flow of viscoelastic fluid over an exponentially stretching surface with variable thermal conductivity (2016)
  19. Ashraf, M. Bilal; Hayat, T.; Alsaedi, A.: Radiative mixed convection flow of an Oldroyd-B fluid over an inclined stretching surface (2016)
  20. Hayat, T.; Imtiaz, M.; Alsaedi, A.: Boundary layer flow of Oldroyd-B fluid by exponentially stretching sheet (2016)

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