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. Kumbhakar, Manotosh: Streamwise velocity profile in open-channel flow based on Tsallis relative entropy (2020)
  2. Kumbhakar, Manotosh; Ghoshal, Koeli; Singh, Vijay P.: Two-dimensional distribution of streamwise velocity in open channel flow using maximum entropy principle: incorporation of additional constraints based on conservation laws (2020)
  3. Nave, OPhir; Sharma, Manju: Singular perturbed vector field (SPVF) applied to complex ODE system with hidden hierarchy application to turbocharger engine model (2020)
  4. Niazi, M. D. K.; Xu, Hang: Modelling two-layer nanofluid flow in a micro-channel with electro-osmotic effects by means of Buongiorno’s model (2020)
  5. Rahman, Mujeeb Ur; Khan, M. Ijaz; Haq, Fazal; Hayat, T.; Khan, M. Imran: A shear flow investigation for incompressible second grade nanomaterial: derivation and analytical solution of model (2020)
  6. Ray, Atul Kumar; Vasu, B.; Murthy, P. V. S. N.; Gorla, Rama S. R.: Non-similar solution of Eyring-Powell fluid flow and heat transfer with convective boundary condition: homotopy analysis method (2020)
  7. Sacramento, Marta; Almeida, Cecília; Moreira, Miguel: IFOHAM -- a generalization of the Picard-Lindelöf iteration method (2020)
  8. Wang, Anyang; Xu, Hang; Yu, Qiang: Homotopy coiflets wavelet solution of electrohydrodynamic flows in a circular cylindrical conduit (2020)
  9. Wang, Ping; Wang, Yongyan; Huo, Xintai: Nonlinear hydroelastic interaction among a floating elastic plate, water waves, and exponential shear currents (2020)
  10. Zhang, Guoqi; Wu, Zhiqiang: Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives (2020)
  11. Zhao, Qingkai; Xu, Hang; Tao, Longbin: Flow and heat transfer of nanofluid through a horizontal microchannel with magnetic field and interfacial electrokinetic effects (2020)
  12. Zhou, Yang; Wu, Baisheng; Lim, C. W.; Sun, Weipeng: Analytical approximations to primary resonance response of harmonically forced oscillators with strongly general nonlinearity (2020)
  13. Alamri, Sultan Z.; Khan, Ambreen A.; Azeez, Mariam; Ellahi, R.: Effects of mass transfer on MHD second grade fluid towards stretching cylinder: a novel perspective of Cattaneo-Christov heat flux model (2019)
  14. Alipour, M.; Vali, M. A.; Borzabadi, A. H.: A hybrid parametrization approach for a class of nonlinear optimal control problems (2019)
  15. Bibi, Aneela; Xu, Hang: Entropy generation analysis of peristaltic flow and heat transfer of a Jeffery nanofluid in a horizontal channel under magnetic environment (2019)
  16. Eltayeb, Hassan; Abdalla, Yahya T.; Bachar, Imed; Khabir, Mohamed H.: Fractional telegraph equation and its solution by natural transform decomposition method (2019)
  17. Ghiasi, Emran Khoshrouye; Saleh, Reza: On approximation of FBVP by homotopy-based truncation technique (2019)
  18. Hayat, T.; Kiyani, M. Z.; Ahmad, I.; Alsaedi, A.: Double stratified radiative flow of an Oldroyd-B nanofluid with nonlinear convection (2019)
  19. Jangili, Srinivas; Adesanya, Samuel Olumide; Ogunseye, Hammed Abiodun; Lebelo, Ramoshweu: Couple stress fluid flow with variable properties: a second law analysis (2019)
  20. Khoshrouye Ghiasi, Emran; Saleh, Reza: A convergence criterion for tangent hyperbolic fluid along a stretching wall subjected to inclined electromagnetic field (2019)

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