The Runge Kutta Applet allows you to solve an Initial Value Problem. In an initial value problem, the behavior of a system is described by an ordinary differential equation of the form
where is a known function we can evaluate given x and y. It is straight forward to visualize this differential equation with a vector field: the gradient can be evaluated at each point in the x-y-plane using the equation above.
To completely specify the problem, it is necesary to give an initial value for x and y. In the following example we use the initial values x=0, y=0 and get the integral curve displayed in pink. This curve is the solution of the Initial Value Problem.