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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

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