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 195 articles , 1 standard article )

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  1. 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)
  2. Zhang, Guoqi; Wu, Zhiqiang: Homotopy analysis method for approximations of Duffing oscillator with dual frequency excitations (2019)
  3. Baxter, Mathew; Dewasurendra, Mangalagama; Vajravelu, Kuppalapalle: A method of directly defining the inverse mapping for solutions of coupled systems of nonlinear differential equations (2018)
  4. 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)
  5. 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)
  6. Faghidian, S. Ali: Reissner stationary variational principle for nonlocal strain gradient theory of elasticity (2018)
  7. Fu, H. X.; Qian, Y. H.: Study on a multi-frequency homotopy analysis method for period-doubling solutions of nonlinear systems (2018)
  8. Geethamalini, S.; Balamuralitharan, S.: Semianalytical solutions by homotopy analysis method for EIAV infection with stability analysis (2018)
  9. Khurshudyan, Asatur Zh.: Heuristic determination of resolving controls for exact and approximate controllability of nonlinear dynamic systems (2018)
  10. Liu, Z.; Xu, D. L.; Liao, S. J.: Finite amplitude steady-state wave groups with multiple near resonances in deep water (2018)
  11. Mahmoudpour, E.; Hosseini-Hashemi, S. H.; Faghidian, S. A.: Nonlinear vibration analysis of FG nano-beams resting on elastic foundation in thermal environment using stress-driven nonlocal integral model (2018)
  12. Nave, Ophir; Elbaz, Miriam: Combination of singularly perturbed vector field method and method of directly defining the inverse mapping applied to complex ODE system prostate cancer model (2018)
  13. Nave, Ophir; Elbaz, Miriam: Method of directly defining the inverse mapping applied to prostate cancer immunotherapy -- mathematical model (2018)
  14. Noeiaghdam, Samad; Suleman, Muhammad; Budak, Hüseyin: Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method (2018)
  15. Saberi Najafi, H.; Edalatpanah, S. A.; Refahisheikhani, A. H.: An analytical method as a preconditioning modeling for systems of linear equations (2018)
  16. Seth, G. S.; Mishra, M. K.; Tripathi, R.: Modeling and analysis of mixed convection stagnation point flow of nanofluid towards a stretching surface: OHAM and FEM approach (2018)
  17. Singh, Randhir: Optimal homotopy analysis method for the non-isothermal reaction-diffusion model equations in a spherical catalyst (2018)
  18. Turkyilmazoglu, M.: Convergence accelerating in the homotopy analysis method: a new approach (2018)
  19. Yang, Xiaoyan; Dias, Frederic; Liao, Shijun: On the steady-state resonant acoustic-gravity waves (2018)
  20. Yang, Zhaochen; Liao, Shijun: On the generalized wavelet-Galerkin method (2018)

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