Finding multiple solutions of nonlinear problems by means of the homotopy analysis method

Using the boundary layer flows over a permeable plate as an example, we show that the homotopy analysis method (HAM) can be applied to give series solutions of all branches of multiple solutions, even if these multiple solutions are very close and thus rather difficult to distinct even by numerical techniques. A new branch of solutions is found, which has never been reported. This indicates that the homotopy analysis method is a powerful tool for strongly nonlinear problems, especially for those having multiple solutions. © 2006, China Ship Scientific Research Center.