1st order differential equation
A vector field is defined by a function f(x,y) and the associated differential equation y'=f(x,y) is numerically integrated, both by the Euler method and by the Runge-Kutta method 2. The initial condition as well as the discretization step and the extent of the vector field are modifiable. The function f(x,y) can be chosen from a series of examples (to be enriched) or typed on the keyboard.
Identify systematic errors made by both methods. Vary the starting point and the discretization step. Enrich the library of explicit solutions.