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 184 articles , 1 standard article )

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  1. Georgieva, Atanaska: Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method (2021)
  2. Kumbhakar, Manotosh; Ray, Rajendra K.; Chakraborty, Suvra Kanti; Ghoshal, Koeli; Singh, Vijay P.: Mathematical modelling of streamwise velocity profile in open channels using Tsallis entropy (2021)
  3. Rana, Puneet; Shukla, Nisha; Bég, O. Anwar; Bhardwaj, Anuj: Lie group analysis of nanofluid slip flow with Stefan blowing effect via modified Buongiorno’s model: entropy generation analysis (2021)
  4. Chen, Qing-Bo; Xu, Hang: Coiflet wavelet-homotopy solution of channel flow due to orthogonally moving porous walls governed by the Navier-Stokes equations (2020)
  5. Grinberg, I.; Matlack, K. H.: Nonlinear elastic wave propagation in a phononic material with periodic solid-solid contact interface (2020)
  6. Ishaq, M.; Xu, Hang: Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma (2020)
  7. Khan, Hassan; Khan, Adnan; Al Qurashi, Maysaa; Baleanu, Dumitru; Shah, Rasool: An analytical investigation of fractional-order biological model using an innovative technique (2020)
  8. Kumbhakar, Manotosh: Streamwise velocity profile in open-channel flow based on Tsallis relative entropy (2020)
  9. 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)
  10. Nave, OPhir; Sharma, Manju: Singular perturbed vector field (SPVF) applied to complex ODE system with hidden hierarchy application to turbocharger engine model (2020)
  11. 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)
  12. Sacramento, Marta; Almeida, Cecília; Moreira, Miguel: IFOHAM -- a generalization of the Picard-Lindelöf iteration method (2020)
  13. Wang, Anyang; Xu, Hang; Yu, Qiang: Homotopy coiflets wavelet solution of electrohydrodynamic flows in a circular cylindrical conduit (2020)
  14. Zhang, Guoqi; Wu, Zhiqiang: Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives (2020)
  15. Zhao, Qingkai; Xu, Hang; Tao, Longbin: Flow and heat transfer of nanofluid through a horizontal microchannel with magnetic field and interfacial electrokinetic effects (2020)
  16. 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)
  17. Alipour, M.; Vali, M. A.; Borzabadi, A. H.: A hybrid parametrization approach for a class of nonlinear optimal control problems (2019)
  18. 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)
  19. Eltayeb, Hassan; Abdalla, Yahya T.; Bachar, Imed; Khabir, Mohamed H.: Fractional telegraph equation and its solution by natural transform decomposition method (2019)
  20. Ghiasi, Emran Khoshrouye; Saleh, Reza: On approximation of FBVP by homotopy-based truncation technique (2019)

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