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 160 articles , 1 standard article )

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  1. Nave, OPhir; Sharma, Manju: Singular perturbed vector field (SPVF) applied to complex ODE system with hidden hierarchy application to turbocharger engine model (2020)
  2. Zhao, Qingkai; Xu, Hang; Tao, Longbin: Flow and heat transfer of nanofluid through a horizontal microchannel with magnetic field and interfacial electrokinetic effects (2020)
  3. 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)
  4. Ghiasi, Emran Khoshrouye; Saleh, Reza: On approximation of FBVP by homotopy-based truncation technique (2019)
  5. Hayat, T.; Kiyani, M. Z.; Ahmad, I.; Alsaedi, A.: Double stratified radiative flow of an Oldroyd-B nanofluid with nonlinear convection (2019)
  6. Jangili, Srinivas; Adesanya, Samuel Olumide; Ogunseye, Hammed Abiodun; Lebelo, Ramoshweu: Couple stress fluid flow with variable properties: a second law analysis (2019)
  7. Khoshrouye Ghiasi, Emran; Saleh, Reza: A convergence criterion for tangent hyperbolic fluid along a stretching wall subjected to inclined electromagnetic field (2019)
  8. Liu, Z.; Xie, D.: Finite-amplitude steady-state wave groups with multiple near-resonances in finite water depth (2019)
  9. Maitama, Shehu; Zhao, Weidong: Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets (2019)
  10. Noeiaghdam, Samad; Fariborzi Araghi, Mohammad Ali; Abbasbandy, Saeid: Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic (2019)
  11. Rana, Puneet; Shukla, Nisha; Gupta, Yogesh; Pop, Ioan: Analytical prediction of multiple solutions for MHD Jeffery-Hamel flow and heat transfer utilizing KKL nanofluid model (2019)
  12. Shafiq, Anum; Sindhu, T. N.; Hammouch, Z.: Characteristics of homogeneous heterogeneous reaction on flow of Walters’ B liquid under the statistical paradigm (2019)
  13. Van Gorder, Robert A.: Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations (2019)
  14. Yavuz, Mehmet; Özdemir, Necati: New numerical techniques for solving fractional partial differential equations in conformable sense (2019)
  15. Yépez-Martínez, H.; Gómez-Aguilar, J. F.: A new modified definition of Caputo-fabrizio fractional-order derivative and their applications to the multi step homotopy analysis method (MHAM) (2019)
  16. Baxter, Mathew; Dewasurendra, Mangalagama; Vajravelu, Kuppalapalle: A method of directly defining the inverse mapping for solutions of coupled systems of nonlinear differential equations (2018)
  17. Cui, Jifeng; Zhang, Wenyu; Liu, Zeng; Sun, Jianglong: On the limit cycles, period-doubling, and quasi-periodic solutions of the forced van der Pol-Duffing oscillator (2018)
  18. Dewasurendra, Mangalagama; Baxter, Mathew; Vajravelu, Kuppalapalle: A method of directly defining the inverse mapping for solutions of non-linear coupled systems arising in convection heat transfer in a second grade fluid (2018)
  19. Faghidian, S. Ali: Reissner stationary variational principle for nonlocal strain gradient theory of elasticity (2018)
  20. Fu, H. X.; Qian, Y. H.: Study on a multi-frequency homotopy analysis method for period-doubling solutions of nonlinear systems (2018)

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