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. Sharma, Kalpna; Gupta, Sumit: Homotopy analysis solution to thermal radiation effects on MHD boundary layer flow and heat transfer towards an inclined plate with convective boundary conditions (2017)
  2. 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)
  3. Srivastava, H. M.; Kumar, Devendra; Singh, Jagdev: An efficient analytical technique for fractional model of vibration equation (2017)
  4. Vajravelu, K.; Prasad, K. V.; Vaidya, Hanumesh; Basha, Neelufer Z.; Ng, Chiu-On: Mixed convective flow of a Casson fluid over a vertical stretching sheet (2017)
  5. Van Gorder, Robert A.: On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations (2017)
  6. Wang, Ping; Wang, Yongyan; Su, Chuanqi; Yang, Yanzhao: Nonlinear hydroelastic waves generated due to a floating elastic plate in a current (2017)
  7. Yang, Zhaochen; Liao, Shijun: A HAM-based wavelet approach for nonlinear ordinary differential equations (2017)
  8. Yang, Zhaochen; Liao, Shijun: A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application (2017)
  9. Zhang, Xiaolong; Liang, Songxin; Zou, Li: Uniqueness and error estimates for solutions to higher-order boundary value problems (2017)
  10. Zhong, Xiaoxu; Liao, Shijun: On the homotopy analysis method for backward/forward-backward stochastic differential equations (2017)
  11. Zhong, X. X.; Liao, S. J.: Analytic solutions of Von Kármán plate under arbitrary uniform pressure -- equations in differential form (2017)
  12. 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)
  13. Ashraf, M. Bilal; Hayat, T.; Alsaedi, A.: Radiative mixed convection flow of an Oldroyd-B fluid over an inclined stretching surface (2016)
  14. Bakkyaraj, T.; Sahadevan, R.: Approximate analytical solution of two coupled time fractional nonlinear Schrödinger equations (2016)
  15. Brociek, Rafał; Hetmaniok, Edyta; Matlak, Jarosław; Słota, Damian: Application of the homotopy analysis method for solving the systems of linear and nonlinear integral equations (2016)
  16. Gómez-Aguilar, J. F.; Torres, L.; Yépez-Martínez, H.; Baleanu, D.; Reyes, J. M.; Sosa, I. O.: Fractional Liénard type model of a pipeline within the fractional derivative without singular kernel (2016)
  17. Gómez-Aguilar, J. F.; Yépez-Martínez, H.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Reyes, J. M.; Sosa, I. O.: Series solution for the time-fractional coupled mkdv equation using the homotopy analysis method (2016)
  18. Hayat, T.; Imtiaz, M.; Alsaedi, A.: Boundary layer flow of Oldroyd-B fluid by exponentially stretching sheet (2016)
  19. Hayat, T.; Shafiq, A.; Alsaedi, A.; Shahzad, S. A.: Unsteady MHD flow over exponentially stretching sheet with slip conditions (2016)
  20. Hendi, F. A.; Kashkari, B. S.; Alderremy, A. A.: The variational homotopy perturbation method for solving (((n\timesn)+1)) dimensional Burgers’ equations (2016)

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