Runge-Kutta Methods Calculator

Runge-Kutta Methods Calculator is an online application on Runge-Kutta methods for solving systems of ordinary differential equations at initals value problems given by

y' = f(x, y)


Simply enter your system of equations and initial values as follows:

0) Select the Runge-Kutta method desired in the dropdown on the left labeled as "Choose method" and select in the check box if you want to see all the steps or just the end result.

1) Enter the initial value for the independent variable, x0.
2) Enter the final value for the independent variable, xn.
3) Enter the step size for the method, h.
4) Enter the given initial value of the independent variable y0. Note that if you press "Add Dimension" another row is added and will be two dependent variables
5) Enter the function fx, y) of your problem. Note that if you press "Add Dimension" is added to another row and will be introducing two functions. Some examples are
if f(x,y) = e2xy -> enter e^(2*x*y)
if f(x,y) = sin e2xy -> enter sin(e^(2*x*y))

6) Enter exact solution if known for the estimation of statistical Runge-Kutta methods error. Note again that if you press "Add Dimension" is added to another row and will be introducing two functions.


To begin the calculations simply click "Execute": After a few seconds, a window opens showing the final solution founded by the Runge-Kutta selected and execution statistics.

Final Comments

Runge-Kutta Methods Calculator is restricted about the dimension of the problem to systems of equations 5 and that the accuracy in calculations is 16 decimal digits.
At the same time the maximum processing time for normal ODE is 20 seconds, after that time if no solution is found, it will stop the execution of the Runge-Kutta in operation for over execution times please use the applet in the same web.
Runge-Kutta Methods Calculator does not require installation of any kind, just a browser with javascript support

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Post from other users


2020-02-18 00:41:26

I extremely like the web app, it's so useful and faster;
I have a suggestion : if you can add an export button so we can save the iterations to EXCEL format maybe?
I think that's will be a cool addon!


2020-02-19 15:11:26
Hello, Mohand.

Thanks for your apportation.
It is very interesting, as you say it will be a cool addon. I will work on this next days.
Please give a week.

Carlos Toro


2021-05-29 13:38:39
would you please tell me how solve Runge-Kutta order 3 thank you in advance


2021-05-29 15:42:31
Hi Betty.
You have the Heun O(3) Runke-Kutta Method here in this application, it has order 3.


2021-06-02 23:25:38
This is very useful for my calculus class, one thing though, I wanted to graph the points of (x_n,y_n) rather than view the accuracy of the method. Specifically using the methods of Eulers and Rk4. Still, great widget!

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