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 111 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. Baxter, Mathew; Dewasurendra, Mangalagama; Vajravelu, Kuppalapalle: A method of directly defining the inverse mapping for solutions of coupled systems of nonlinear differential equations (2018)
  3. 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)
  4. Faghidian, S. Ali: Reissner stationary variational principle for nonlocal strain gradient theory of elasticity (2018)
  5. Fu, H. X.; Qian, Y. H.: Study on a multi-frequency homotopy analysis method for period-doubling solutions of nonlinear systems (2018)
  6. Nave, Ophir; Elbaz, Miriam: Method of directly defining the inverse mapping applied to prostate cancer immunotherapy -- mathematical model (2018)
  7. Noeiaghdam, Samad; Suleman, Muhammad; Budak, Hüseyin: Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method (2018)
  8. Saberi Najafi, H.; Edalatpanah, S. A.; Refahisheikhani, A. H.: An analytical method as a preconditioning modeling for systems of linear equations (2018)
  9. 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)
  10. Yang, Xiaoyan; Dias, Frederic; Liao, Shijun: On the steady-state resonant acoustic-gravity waves (2018)
  11. Yang, Zhaochen; Liao, Shijun: On the generalized wavelet-Galerkin method (2018)
  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. Najafi, Ramin; Küçük, Gökçe Dilek; Çelik, Ercan: Modified iteration method for solving fractional gas dynamics equation (2017)
  16. Ouyang, Cheng; Zhu, Min; Mo, Jiaqi: A class of epidemic virus transmission population dynamic system (2017)
  17. Pandey, Rishi Kumar; Mishra, Hradyesh Kumar: Homotopy analysis Sumudu transform method for time -- fractional third order dispersive partial differential equation (2017)
  18. Sharma, Kalpna; Gupta, Sumit: Homotopy analysis solution to thermal radiation effects on MHD boundary layer flow and heat transfer towards an inclined plate with convective boundary conditions (2017)
  19. Shehzad, S. A.; Hayat, T.; Alsaedi, A.; Meraj, M. A.: Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid (2017)
  20. Vajravelu, K.; Prasad, K. V.; Vaidya, Hanumesh; Basha, Neelufer Z.; Ng, Chiu-On: Mixed convective flow of a Casson fluid over a vertical stretching sheet (2017)

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