I'm familiar with explicit numerical methods for solving ODE including Euler's method, and even Runge-Kutta methods (2nd and 4th order).
But I'm really confused when it comes to implicit methods. I understood the ''simplest'' implicit method, being Euler's backward method. I even did a code with it on Matlab and it worked just fine.
But, what about implicit Runge-Kutta 2nd order? How can I get the K's that would make it implicit? I've been searching for examples and can't find anything. It would really help if I saw a solution using an implicit RK-2 for a ODE. Is there any book/paper or anything?
Let's say we have this simple ODE: Y' = -2Y How would an implicit RK-2 work here?