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I need a little help on how does the iteration process. I know how Runge-Kutta 4 works, but I don't know how this Fehlberg one does.

So apparently the iteration goes like this:

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_2.gif [Broken]

Then apparently, the scheme requires two iterations; first would be

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_3.gif [Broken]

The second would be

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_4.gif [Broken]

My question is: what the freaking hell is this lol

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_5.gif [Broken]

As far as I understand this s thing is supposed to correct the value for h, given a value of ε.

My question are,

(1) How do I get the new value of h?

(2) Isn't this the value of h to be used in the next iteration, since I read from some texts that h is to be modified such that given a differential equation that doesn't behave very well, it's for accuracy purposes?

(3) Further, how does the value of ε really work? I know I have to enter the value of ε, and it apparently assigns the degree of accuracy, or so I've heard. But I want to understand this, really. Say for example, my tolerance is 0.84. How different is this from using a tolerance of 0.5? More accurate or less accurate?

This isn't an assignment guys, I just want something new instead of the old RK4 method that requires ridiculously small stepsizes to retain significant accuracy vs. indecently behaving equations. Needless to say, I've been using RK4 blindly with epicly small setpsize just to make sure that I get an accurate answer (which is fairly pathetic).

Thanks and more power guys! :)

So apparently the iteration goes like this:

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_2.gif [Broken]

Then apparently, the scheme requires two iterations; first would be

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_3.gif [Broken]

The second would be

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_4.gif [Broken]

My question is: what the freaking hell is this lol

http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergMod/Images/RungeKuttaFehlbergMod_gr_5.gif [Broken]

As far as I understand this s thing is supposed to correct the value for h, given a value of ε.

My question are,

(1) How do I get the new value of h?

(2) Isn't this the value of h to be used in the next iteration, since I read from some texts that h is to be modified such that given a differential equation that doesn't behave very well, it's for accuracy purposes?

(3) Further, how does the value of ε really work? I know I have to enter the value of ε, and it apparently assigns the degree of accuracy, or so I've heard. But I want to understand this, really. Say for example, my tolerance is 0.84. How different is this from using a tolerance of 0.5? More accurate or less accurate?

This isn't an assignment guys, I just want something new instead of the old RK4 method that requires ridiculously small stepsizes to retain significant accuracy vs. indecently behaving equations. Needless to say, I've been using RK4 blindly with epicly small setpsize just to make sure that I get an accurate answer (which is fairly pathetic).

Thanks and more power guys! :)

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