Results 1 to 2 of 2

Math Help - Runge Kutta method - 2nd order numerically

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    33

    Runge Kutta method - 2nd order numerically

    I have the differential equation:

    x' = 1 + x^2, where  x(0) = 1



    which I have to solve numerically. The problem is just that I don't understand how the method works, and it's hard to find any good explanations online.

    I would really appriciate it if someone explained how to start, like how do you find x_1?

    The equation is to be solved on the intevall [0; 0.6] using 6 steps, so that the steplenght is 0.1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by jenkki View Post
    I have the differential equation:

    x' = 1 + x^2, where  x(0) = 1


    which I have to solve numerically. The problem is just that I don't understand how the method works, and it's hard to find any good explanations online.

    I would really appriciate it if someone explained how to start, like how do you find x_1?

    The equation is to be solved on the intevall [0; 0.6] using 6 steps, so that the steplenght is 0.1
    You use the equation for the derivative at the initial point to step the solution forward by a half step. Now you use the solution at the half step to calculate the "typical" value of the derivative over the whole step and use this to step the solution forward a whole step from the initial point.

    So in this case we have x'=f(x), and we suppose we have the solution at $$ x_i (the initial conditions give us a starting point). We step forward a half step:

    x^*=x_i+(h/2)f(x_i)

    which gives us out "typical derivative on the step of f(x^*).

    Finally we do the step:

    x_{i+1}=x_i+h f(x^*)

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to derive the Runge Kutta 2nd Order Method?
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 10th 2010, 02:33 PM
  2. Determine the order of a Runge-Kutta method
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 19th 2009, 06:56 AM
  3. Third Order Semi Implicit Runge Kutta Method
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 2nd 2009, 07:33 AM
  4. MATLAB and 4th order Runge Kutta Method
    Posted in the Math Software Forum
    Replies: 0
    Last Post: April 1st 2009, 10:07 AM
  5. Fourth-Order Runge-Kutta Method
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 4th 2009, 05:32 AM

Search Tags


/mathhelpforum @mathhelpforum