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 204 articles , 1 standard article )

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  1. 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)
  2. Nave, Ophir; Elbaz, Miriam: Method of directly defining the inverse mapping applied to prostate cancer immunotherapy -- mathematical model (2018)
  3. Noeiaghdam, Samad; Suleman, Muhammad; Budak, Hüseyin: Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method (2018)
  4. Saberi Najafi, H.; Edalatpanah, S. A.; Refahisheikhani, A. H.: An analytical method as a preconditioning modeling for systems of linear equations (2018)
  5. 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)
  6. Singh, Randhir: Optimal homotopy analysis method for the non-isothermal reaction-diffusion model equations in a spherical catalyst (2018)
  7. Turkyilmazoglu, M.: Convergence accelerating in the homotopy analysis method: a new approach (2018)
  8. Yang, Xiaoyan; Dias, Frederic; Liao, Shijun: On the steady-state resonant acoustic-gravity waves (2018)
  9. Yang, Zhaochen; Liao, Shijun: On the generalized wavelet-Galerkin method (2018)
  10. Askari, Amir R.; Tahani, Masoud; Moeenfard, Hamid: A frequency criterion for doubly clamped beam-type N/MEMS subjected to the van der Waals attraction (2017)
  11. Ateş, I.; Zegeling, P. A.: A homotopy perturbation method for fractional-order advection-diffusion-reaction boundary-value problems (2017)
  12. Gómez-Aguilar, J. F.; Yépez-Martínez, H.; Torres-Jiménez, J.; Córdova-Fraga, T.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.: Homotopy perturbation transform method for nonlinear differential equations involving to fractional operator with exponential kernel (2017)
  13. Hayat, T.; Kiran, A.; Imtiaz, M.; Alsaedi, A.: Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid (2017)
  14. Jaradat, Ali; Awawdeh, Fadi; Noorani, Mohd Salmi Md: Identification of time-dependent source terms and control parameters in parabolic equations from overspecified boundary data (2017)
  15. Jia, Wenjuan; He, Xiqin; Guo, Liangdong: The optimal homotopy analysis method for solving linear optimal control problems (2017)
  16. Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru: Analytic study of Allen-Cahn equation of fractional order (2017)
  17. Motsa, Sandile S.; Makukula, Zodwa G.: On a bivariate spectral homotopy analysis method for unsteady mixed convection boundary layer flow, heat, and mass transfer due to a stretching surface in a rotating fluid (2017)
  18. Najafi, Ramin; Küçük, Gökçe Dilek; Çelik, Ercan: Modified iteration method for solving fractional gas dynamics equation (2017)
  19. Ouyang, Cheng; Zhu, Min; Mo, Jiaqi: A class of epidemic virus transmission population dynamic system (2017)
  20. Pandey, Rishi Kumar; Mishra, Hradyesh Kumar: Homotopy analysis Sumudu transform method for time-fractional third order dispersive partial differential equation (2017)

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