Stability for Nonlinear Numerical Scheme
It is usual for the application of Von Neumann or matrix methods in the stability analysis of a numerical scheme for a linear PDE. But Neuman method can only be used for linear problems. For nonlinear problem, for example Du/Dt = (1/2)D(uu)/Dx  32 (Du/Dx)^2+D^2u/Dx^2, Neuman method can not be used. How do we do the stability analysis for this kind of nonliear PDE after disretization, or where can I get reference materials on this issue?
Thank you! 
Re: Stability for Nonlinear Numerical Scheme
If you write the discretized nonlinear equation assuming a first order perturbation
U=U0+deltaU you can linearize the equation (after the discretization). WOuld that help you ? Patrick 
Re: Stability for Nonlinear Numerical Scheme
This problem was addressed by Poinsot and Candel for the inviscid BurgersEquation in Journal of Computational Physics, vol. 62, 282296, 1986.

Re: Stability for Nonlinear Numerical Scheme
Culbert Laney discussed this in great detail in Chapters 15 and 16 of his book Computational Gasdynamics. In fact the linear stability is still relevant.

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