When estimating the solution to an ordinary differential equation, how can you tell if your difference scheme is stable? For example, consider the following scheme: $ u_{i+1} = 2u_{i} + hf(x_i,u_i), $ where h is the size of a single step. Is this scheme stable?
I don't understand the definition of stability so I think an example would help me visualize what I am supposed to do. Thanks!