# Runge–Kutta method

This online calculator implements the Runge-Kutta method, a fourth-order numerical method to solve the first-degree differential equation with a given initial value.

You can use this calculator to solve first-degree differential equation with a given initial value using **the Runge-Kutta method** AKA **classic Runge-Kutta method** (because there is a family of Runge-Kutta methods) or **RK4** (because it is a fourth-order method).

To use this method, you should have differential equation in the form

and enter the right side of the equation *f(x,y)* in the *y'* field below.

You also need initial value as

and the point for which you want to approximate the value.

The last parameter of a method - a step size, is a step to compute the next approximation of a function curve.

Method details can be found below the calculator.

### The Runge-Kutta method

Just like Euler method and Midpoint method, the Runge-Kutta method is a numerical method that starts from an initial point and then takes a short step forward to find the next solution point.

The formula to compute the next point is

where *h* is step size and

The local truncation error of RK4 is of order , giving a global truncation error of order .

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