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. Han, Yu Du; Yun, Jae Heon: Performance of restarted homotopy perturbation method for TV-based image denoising problem (2015)
  2. Haussermann, John; Van Gorder, Robert A.: Efficient low-error analytical-numerical approximations for radial solutions of nonlinear Laplace equations (2015)
  3. Hayat, Tasawar; Muhammad, Taseer; Shehzad, Sabir Ali; Alsaedi, A.: Soret and Dufour effects in three-dimensional flow over an exponentially stretching surface with porous medium, chemical reaction and heat source/sink (2015)
  4. Hayat, T.; Ashraf, M. Bilal; Alsaedi, A.; Alhothuali, M. S.: Soret and Dufour effects in three-dimensional flow of Maxwell fluid with chemical reaction and convective condition (2015)
  5. Hayat, T.; Muhammad, T.; Shehzad, S. A.; Alsaedi, A.: Three-dimensional boundary layer flow of Maxwell nanofluid: mathematical model (2015)
  6. Hetmaniok, Edyta; Słota, Damian; Wituła, Roman; Zielonka, Adam: Solution of the one-phase inverse Stefan problem by using the homotopy analysis method (2015)
  7. Raees, A.; Xu, Hang; Sun, Qiang; Pop, I.: Mixed convection in gravity-driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms (2015)
  8. Saha Ray, S.; Sahoo, S.: A comparative study on the analytic solutions of fractional coupled sine-Gordon equations by using two reliable methods (2015)
  9. Sajid, M.; Arshad, Ambreen; Javed, T.; Abbas, Z.: Stagnation point flow of Walters’ B fluid using hybrid homotopy analysis method (2015)
  10. Van Gorder, Robert A.: The variational iteration method is a special case of the homotopy analysis method (2015)
  11. Wang, Ping: The nonlinear hydroelastic response of a semi-infinite elastic plate floating on a fluid due to incident progressive waves (2015)
  12. Xuan, Chen; Ding, Shurong; Huo, Yongzhong: Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations (2015)
  13. Xu, Dali; Cui, Jifeng; Liao, Shijun; Alsaedi, A.: A HAM-based analytic approach for physical models with an infinite number of singularities (2015)
  14. Xu, Dali; Lin, Zhiliang; Liao, Shijun: Equilibrium states of class-I Bragg resonant wave system (2015)
  15. Yu, Bo; Jiang, Xiaoyun; Xu, Huanying: A novel compact numerical method for solving the two-dimensional non-linear fractional reaction-subdiffusion equation (2015)
  16. Yu, C. H.; Sheu, Tony W. H.; Chang, C. H.; Liao, S. J.: Development of a numerical phase optimized upwinding combined compact difference scheme for solving the Camassa-Holm equation with different initial solitary waves (2015)
  17. Zhao, Qingkai; Xu, Hang; Fan, Tao: Analysis of three-dimensional boundary-layer nanofluid flow and heat transfer over a stretching surface by means of the homotopy analysis method (2015)
  18. Zhu, Jing; Yang, Dan; Zheng, Liancun; Zhang, Xinxin: Second-order slip effects on heat transfer of nanofluid with Reynolds model of viscosity in a coaxial cylinder (2015)
  19. Zou, Keguan; Nagarajaiah, Satish: An analytical method for analyzing symmetry-breaking bifurcation and period-doubling bifurcation (2015)
  20. Zou, Keguan; Nagarajaiah, Satish: The solution structure of the Düffing oscillator’s transient response and general solution (2015)

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