BVPh

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. Fardi, Mojtaba; Kazemi, Ebrahim; Ezzati, Reza; Ghasemi, Mehdi: Periodic solution for strongly nonlinear vibration systems by using the homotopy analysis method (2012)
  2. Ghoreishi, Mohammad; Ismail, Ahmad Izani B. Md.; Rashid, Abdur: The one step optimal homotopy analysis method to circular porous slider (2012)
  3. Kurulay, Muhammet: Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method (2012)
  4. Liao, Shijun: Homotopy analysis method in nonlinear differential equations (2012)
  5. Secer, Aydin; Akinlar, Mehmet Ali; Cevikel, Adem: Efficient solutions of systems of fractional PDEs by the differential transform method (2012)
  6. Golbabai, A.; Sayevand, K.: Analytical modelling of fractional advection-dispersion equation defined in a bounded space domain (2011)
  7. Golbabai, A.; Sayevand, K.: Analytical treatment of differential equations with fractional coordinate derivatives (2011)
  8. Hayat, T.; Mustafa, M.; Hendi, A. A.: Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet (2011)
  9. Hayat, T.; Sajjad, R.; Abbas, Z.; Sajid, M.; Hendi, Awatif A.: Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium (2011)
  10. Heibig, Arnaud; Palade, Liviu Iulian: Well posedness of a linearized fractional derivative fluid model (2011)
  11. Liu, Jincun; Hou, Guolin: Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method (2011)
  12. Mustafa, M.; Hayat, T.; Pop, I.; Asghar, S.; Obaidat, S.: Stagnation-point flow of a nanofluid towards a stretching sheet (2011)
  13. You, Xiangcheng; Xu, Hang: Analytical approximations for the periodic motion of the Duffing system with delayed feedback (2011)
  14. Abbasbandy, Saeid; Shirzadi, A.: Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems (2010)
  15. Hayat, T.; Mustafa, M.; Asghar, S.: Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction (2010)
  16. Hayat, T.; Mustafa, M.; Pop, I.: Heat and mass transfer for Sorét and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid (2010)
  17. Hayat, T.; Sajjad, R.; Asghar, S.: Series solution for MHD channel flow of a Jeffery fluid (2010)
  18. Kurulay, Muhammet; Bayram, Mustafa: Approximate analytical solution for the fractional modified Kdv by differential transform method (2010)
  19. Yuan, Peixin; Li, Yongqiang: Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method (2010)
  20. Alomari, A. K.; Noorani, M. S. M.; Nazar, R.: Solution of delay differential equation by means of homotopy analysis method (2009)

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