1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Numerical Solution of Differential equation

  1. Apr 11, 2014 #1

    wel

    User Avatar
    Gold Member

    The nonlinear oscillator [itex]y'' + f(y)=0[/itex] is equivalent to the
    Simple harmonic motion:
    [itex]y'= -z [/itex],
    [itex]z'= f(y)[/itex]

    the modified Symplectic Euler equation are

    [itex]y'=-z+\frac {1}{2} hf(y)[/itex]

    [itex]y'=f(y)+\frac {1}{2} hf_y z[/itex]

    and deduce that the coresponding approximate solution lie on the family of curves
    [itex]2F(y)-hf(y)y+z^2=constant[/itex]

    where [itex]F_y= f(y)[/itex].


    ans =>

    for the solution of the system lie on the family of curves, i was thinking


    [itex]\frac{d}{dt}[2F(y)-hf(y)y+z^2]= y \frac{dy}{dt} + z \frac{dz}{dt}[/itex]
    [itex]=y(-z+\frac{1}{2} hf(y)) +z(f(y)- \frac{1}{2} h f_y z)[/itex]
    but I can not do anything after that to get my answer constant.


    can any genius people please help me
     
  2. jcsd
  3. Apr 19, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    How did you get on?
    Nice to show some sort of attempt, but please show your reasoning.

    If you are supposed to deduce that family of curves, perhaps you shouldn't be starting with them.
    Though attempting to work the problem backwards from the solution can help you figure it out.

    Start with the modified symplectic euler equations.
    Check your course notes about them - how would you go about getting the "corresponding approximate solution" for those?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted