Homotopy Analysis Method (or Homotopy Perturbation Method)?

[crackjack]

Homotopy Analysis Method (or Homotopy Perturbation Method)??

How effective is this Homotopy Analysis Method (HAM) in solving coupled non-linear PDE? I see some papers, but they seem to be cross-referencing a small group of people most of the time. This sounds strange for a method that is so generic and so powerful (and has been around since 1992), as those papers all say.

Homotopy Perturbation Method (HPM) is a recent variant of HAM. But this also seems to suffer from the same strange behaviors as HAM's papers.

 

[HallsofIvy]

"HAM" and "HPM" are methods for finding approximate solutions to non-linear equations. The WKB method used in Quantum Mechanics to solve Shrodinger's equation is an example of a "HPM".

 

[crackjack]

Thanks for the reply.

I understand that it is an approximation method. But the difference from WKB seems to be that, in HAM, there is no apriori need for a small-parameter (with which to perturb). HAM introduces an artificial parameter with which a perturbation solution is constructed and then the parameter is taken to unity. The convergence of the solution is controlled by another parameter.

I want to know if HAM really brings something powerful to the table and, if so, why do I not see it beyond a relatively small self-referencing group.

 

[hunt_mat]

I will ask my supervisor this, as he is an authority on this kind of stuff.