H value in runge kutta method 2nd order

[Struggling]

hi can anyone explain to me how to get the H value for runge kutta second method? I've searched everywhere online but i just don't understand it.

if found h = tn - to/n??

i know what value of "to" is but no clue what values to put in for n and tn?

thanks

 

[Integral]

If I am interpreting what you are saying correctly, h is your time step, the errors of a 2nd order RK method are on the order of h⁵. It looks to me like your t₀ is the starting time, therefore t_n is the time end point, n is the number of time steps you are taking so your h is the time interval divided by the number of time steps.

for example let:
t₀=0
t_n=100
n=1000

$$h = \frac {t_n - t_0} n = \frac {100 - 0} {1000} = .1$$

 

[tacman]

The H value in the Runge Kutta method for second order is the step size or the interval between each calculation of the function. This value is determined by dividing the total time interval (tn - to) by the number of steps (n).

To calculate the H value, you need to know the initial time (to) and the final time (tn), as well as the number of steps (n) you want to take in between. This number is usually determined based on the desired precision and accuracy of the solution.

For example, if you have a total time interval of 10 seconds and you want to take 100 steps in between, then the H value would be 10/100 = 0.1 seconds. This means that the function will be calculated at every 0.1 second interval to get a more accurate solution.

In summary, the H value is determined by dividing the total time interval by the number of steps, and this value is used to calculate the function at each step in the Runge Kutta method for second order. I hope this explanation helps you understand how to get the H value for this method.