Introduction to the Homotopy Analysis Method
- Part I Basic Ideas
- Introduction
- Illustrative description
- Systematic description
- Relations to some previous analytic methods
- Advantages, limitations, and open questions
- Part II Applications
- Simple bifurcation of a nonlinear problem
- Homotopy analysis solution
- Zero-order deformation equation
- Homotopy analysis solution
- Multiple solutions of a nonlinear problem
- Nonlinear eigenvalue problem
- Thomas-Fermi atom model
- Volterra’s population model
- Free oscillation systems with odd nonlinearity
- Free oscillation systems with quadratic nonlinearity
- Limit cycle in a multidimensional system
- Blasius’ viscous flow
- Boundary-layer flows with exponential property
- Boundary-layer flows with algebraic property
- Von K’arm´an swirling viscous flow
- Homotopy analysis solution
- Zero-order deformation equation
- High-order deformation equation
- Homotopy analysis solution
- Nonlinear progressive waves in deep water
- Homotopy analysis solution
- Zero-order deformation equation
- High-order deformation equation
- Homotopy analysis solution
- Simple bifurcation of a nonlinear problem