1Applied Science School, University of Science and Technology Beijing, Beijing 100083, China. E-mail: liancunzheng@sina.com
2Mechanical Engineering School, University of Science and Technology, Beijing, Beijing 100083, China. E-mail: cxh2002683@sohu.com
AMS subject classification: 34A34.
A new definition of the homotopy analysis method is given by means of the decomposition method in this paper. The convergence of the homotopy decomposition method is proved under some reasonable hypotheses, which provide the theoretical basis of the homotopy decomposition method for solving nonlinear problems.
Nonlinear equations, decomposition method, solution series, homotopy analysis method
