Advances in the Homotopy Analysis Method

Unlike other analytic techniques, the homotopy analysis method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity. This book, edited by the pioneer and founder of the HAM, describes the current advances of this powerful analytic approximation method for highly nonlinear problems. Coming from different countries and fields of research, the authors of each chapter are top experts in the HAM and its applications.

1. Chance and challenge: a brief review of homotopy analysis method / S.-J. Liao -- 2. Predictor homotopy analysis method (PHAM) / S. Abbasbandy and E. Shivanian -- 3. Spectral homotopy analysis method for nonlinear boundary value problems / S. Motsa and P. Sibanda -- 4. Stability of auxiliary linear operator and convergence-control parameter / R.A. Van Gorder -- 5. A convergence condition of the homotopy analysis method / M. Turkyilmazoglu -- 6. Homotopy analysis method for some boundary layer flows of nanofluids / T. Hayat and M. Mustafa -- 7. Homotopy analysis method for fractional Swift-Hohenberg equation / S. Das and K. Vishal -- 8. HAM-based package NOPH for periodic oscillations of nonlinear dynamic systems / Y.-P. Liu -- 9. HAM-based mathematica package BVPh 2.0 for nonlinear boundary value problems / Y.-L. Zhao and S.-J. Liao.