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Consider the PDE ut + aux = 0. a) Write down a second order accurate central difference scheme and a first order forward in

 

Consider the PDE ut + aux = 0. a) Write down a second order accurate central difference scheme and a first order forward in time scheme. b) Perform a Von Neumann stability analysis for the scheme and comment on stability properties. c) Derive the exact amplification factor exact for the above PDE and comment on the implications.

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