Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homotopy Analysis Method (or Homotopy Perturbation Method)?

  1. Aug 25, 2011 #1
    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.
     
  2. jcsd
  3. Aug 26, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Homotopy Analysis Method (or Homotopy Perturbation Method)??

    "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".
     
  4. Aug 26, 2011 #3
    Re: Homotopy Analysis Method (or Homotopy Perturbation Method)??

    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.
     
  5. Aug 30, 2011 #4

    hunt_mat

    User Avatar
    Homework Helper

    Re: Homotopy Analysis Method (or Homotopy Perturbation Method)??

    I will ask my supervisor this, as he is an authority on this kind of stuff.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Homotopy Analysis Method (or Homotopy Perturbation Method)?
  1. Frobenius Method (Replies: 4)

  2. Euler's Method (Replies: 3)

  3. Frobenius Method (Replies: 3)

Loading...