How to pass a hard coded differential equation through Runge-Kutta 4

Question

I\'m trying to implement Runge-Kutta for example problems dy/dt = y - t^2 + 1 and dy/dt = t * y + t^3 in C# and I cannot seem to get the output I\'m expecting. I have spli

Answer 1

You are doing a classical error in the RK4 implementation: Having two variants to position the multiplication with dt to choose from, you are using both.

It is either

k2 = dt*f(t+0.5*dt, y+0.5*k1)

or

k2 = f(t+0.5*dt, y+0.5*dt*k1)

and analogously in the other lines of the algorithm.