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. Chen, Qing-Bo; Xu, Hang: Coiflet wavelet-homotopy solution of free convection in a closed cavity subjected to an inclined external magnetic field (2022)
  2. Luo, Xin-long; Xiao, Hang; Lv, Jia-hui: Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations (2022)
  3. Wang, An-Yang; Xu, Hang: Highly accurate wavelet-homotopy solutions for mixed convection hybrid nanofluid flow in an inclined square lid-driven cavity (2022)
  4. Wang, Yang; Topputo, Francesco: A TFC-based homotopy continuation algorithm with application to dynamics and control problems (2022)
  5. Aziz, Samaira; Ahmad, Iftikhar; Khan, Sami Ullah; Ali, Nasir: A three-dimensional bioconvection Williamson nanofluid flow over bidirectional accelerated surface with activation energy and heat generation (2021)
  6. Doeva, Olga; Masjedi, Pedram Khaneh; Weaver, Paul M.: Static analysis of composite beams on variable stiffness elastic foundations by the homotopy analysis method (2021)
  7. Georgieva, Atanaska: Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method (2021)
  8. Jafarimoghaddam, A.; Roşca, N. C.; Roşca, A. V.; Pop, I.: The universal Blasius problem: new results by Duan-Rach Adomian decomposition method with Jafarimoghaddam contraction mapping theorem and numerical solutions (2021)
  9. Khuri, S. A.; Sayfy, A.: Numerical solution of a generalized Falkner-Skan flow of a FENE-P fluid (2021)
  10. 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)
  11. Loganathan, K.; Alessa, Nazek; Namgyel, Ngawang; Karthik, T. S.: MHD flow of thermally radiative Maxwell fluid past a heated stretching sheet with Cattaneo-Christov dual diffusion (2021)
  12. Luo, Xin-long; Xiao, Hang: Generalized continuation Newton methods and the trust-region updating strategy for the underdetermined system (2021)
  13. Madhusudhan, R.; Nargund, Achala L.; Sathyanarayana, S. B.: The effect of magnetic field on compressible boundary layer by homotopy analysis method (2021)
  14. 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)
  15. Sahabandu, C. W.; Karunarathna, D.; Sewvandi, P.; Juman, Z. A. M. S.; Dewasurendra, M.; Vajravelu, K.: A method of directly defining the inverse mapping for a nonlinear partial differential equation and for systems of nonlinear partial differential equations (2021)
  16. Wang, Ping; Lu, Dongqiang: Nonlinear hydroelastic waves traveling in a plate in terms of Plotnikov-Toland’s model (2021)
  17. 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)
  18. Grinberg, I.; Matlack, K. H.: Nonlinear elastic wave propagation in a phononic material with periodic solid-solid contact interface (2020)
  19. Ishaq, M.; Xu, Hang: Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma (2020)
  20. Khan, Hassan; Khan, Adnan; Al Qurashi, Maysaa; Baleanu, Dumitru; Shah, Rasool: An analytical investigation of fractional-order biological model using an innovative technique (2020)

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