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 .