dissipative and dispersive error of finite difference methods
Hi all,
We know that for the spatial derivative using a finite difference method, if the leading error term is odd, then the results contain dispersive error, while if the leading error term is even, then it has dissipative error. I want to compare the degree of such errors. Say, the leading error term is 7th order (FD7), compared with the leading error term is 5th order (FD5), which one has more severe dispersive error? For sure, FD7 is more accurate, what's its performance with regard to dispersive error? Thanks. Shu 
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Furthermore, I suggest using the spectral analysis too, that is the modified wavenumber that each formula produces. It is important to remark that not necessarily a higher order accurate formula performs better than a lower one on a given grid. Accuracy order is only an asymptotic estimation that does not tell you how the formula behaves for the chosen grid. Thus, the modified wavenumber analysis can help to understand the error distribution for the grid you want to use. 
There is a standard procedure of analysing dispersive and dissipative behavior of FD schemes. Discretize a linear advection equation, plug in a wave with frequency k and amplitude a and check the resulting frequency and amplitude response  that gives you the dissipation and dispersion error of your scheme.

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Hello Prof. Denaro,
I have only seen this done for linear equations. I assume that Burger's would lead to a nonlinear system to solve for? Do you have any good reference on the details of this? that would be a very interesting read! thanks in advance! 
I don't know if Prof. Denaro is referencing what i have in mind; however, a possible practical (i.e., non analytical) approach is this:
http://www.sciencedirect.com/science...21999111001148 
Thank you Paolo,
that looks very interesting! 
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yes, there are some papers as this one that in these years analysed the nonlinear equations. We also worked on the wavenumberbased analysis for the one and multidimensional nonlinear equations, using an analytical/numerical approach http://onlinelibrary.wiley.com/doi/1...d.179/abstract http://www.sciencedirect.com/science...21999111000933 
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