# Runge-Kutta method (4th-order,1st-derivative) Calculator

## Calculates the solution y=f(x) of the ordinary differential equation y'=F(x,y) using Runge-Kutta fourth-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
 $\normal Runge-Kutta\ method\\[10pt](1)\ y'=F(x,y),\hspace{30} y_0=f(x_0)\rightarrow\ y=f(x)\\(2)\ y_{n+1}=y_n+{\large\frac{1}{6}}(k_1+2k_2+2k_3+k_4)+{\small O}(h^5)\\\vspace{10}\\\hspace{30} k_1=hF(x_n,\ y_n)\\\hspace{30} k_2=hF(x_n+{\large\frac{h}{2}},\ y_n+{\large\frac{k_1}{2}})\\\hspace{30} k_3=hF(x_n+{\large\frac{h}{2}},\ y_n+{\large\frac{k_2}{2}})\\\hspace{30}k_4=hF(x_n+h,\ y_n+k_3)\\$

Runge-Kutta method (4th-order,1st-derivative)
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[1]  2018/12/27 05:20   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Checking calculation
Comment/Request
Show coefficients for each iteration
[2]  2018/12/10 07:23   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Math project
Comment/Request
possibly include example calculations
[3]  2018/11/21 18:56   Male / Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of use
study
[4]  2018/10/03 06:53   Male / 40 years old level / A teacher / A researcher / Very /
Purpose of use
Demonstration in College Classroom
[5]  2018/09/09 23:13   Male / Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of use
Help on a quiz
[6]  2018/07/24 19:33   Male / Under 20 years old / Self-employed people / Very /
Purpose of use
using forth order of runge kutta method with h=1 to compute the approximate solution for y(2) working to 4 decimals places given that y(0)=1 dy/dx x²y
[7]  2018/05/19 20:08   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
To know it well and prepare for exam
[8]  2018/04/29 03:39   Male / 20 years old level / An engineer / Very /
Purpose of use
Homework
[9]  2018/04/24 03:53   Male / 20 years old level / An engineer / Very /
Purpose of use
in syllubus
[10]  2018/03/19 06:54   Male / 60 years old level or over / A teacher / A researcher / - /
Purpose of use
Can this be used for a system of equations?

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