Consider the PDE ut + aux = 0. a) Write down a second order accurate central...

 

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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 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. 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.