# Stability of numerical schemes for difference equations

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!

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I think it would be helpful, both for yourself and for people trying to answer the question, to write down the precise definition of stability that you are working with. – Jitse Niesen Nov 2 '11 at 9:20