# Runge-Kutta method (2nd-order,1st-derivative) Calculator

## Calculates the solution y=f(x) of the ordinary differential equation y'=F(x,y) using Runge-Kutta second-order method.

 The initial condition is y0=f(x0), and the root x is calculated within the range of from x0 to xn. $\normal \\\vspace{10}y'=F(x,y)\hspace{30} y_0=f(x_0)\rightarrow\ y=f(x)\\$

 F(x,y) x0 initial condition y0 = f(x0) xn x0≦x≦xn [ partition n 10 20 50 100 200 500  ] 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Runge-Kutta\ method\\[10pt](1)\ y'=F(x,y),\hspace{30} y_0=f(x_0)\rightarrow\ y=f(x)\\(2)\ y_{n+1}=y_n+k_2+{\small O}(h^3)\\\vspace{10}\\\hspace{30} k_1=hF(x_n,\ y_n)\\\hspace{30} k_2=hF(x_n+{\large\frac{h}{2}},\ y_n+{\large\frac{k_1}{2}})\\$

Runge-Kutta method (2nd-order,1st-derivative)
 [1-5] /5 Disp-Num5103050100200
[1]  2019/03/04 11:49   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Double check python code
[2]  2018/12/04 15:52   Male / 30 years old level / A teacher / A researcher / - /
Purpose of use
research
Comment/Request
please upload the method of 2nd order differential equation
from Keisan
We have uploaded the Runge-Kutta(2nd derivative) calculators.

Runge-Kutta method (2nd-order,2nd-derivative)
https://keisan.casio.com/exec/system/1548125036
Runge-Kutta method (4th-order,2nd-derivative)
https://keisan.casio.com/exec/system/1548128854
[3]  2018/07/19 05:07   Male / 40 years old level / - / Very /
Purpose of use
research
[4]  2017/09/28 02:40   Female / 30 years old level / High-school/ University/ Grad student / Not at All /
Purpose of use
check work
Comment/Request
where is the input for the h value?
[5]  2016/05/06 01:26   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Check values of my code found in matlab

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