# Stability for Nonlinear Numerical Scheme

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 February 1, 2001, 13:34 Stability for Nonlinear Numerical Scheme #1 Guo Guest   Posts: n/a 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!

 February 6, 2001, 10:59 Re: Stability for Nonlinear Numerical Scheme #2 Patrick Godon Guest   Posts: n/a If you write the discretized non-linear equation assuming a first order perturbation U=U0+deltaU you can linearize the equation (after the discretization). WOuld that help you ? Patrick

 February 7, 2001, 12:51 Re: Stability for Nonlinear Numerical Scheme #3 Ralf Massjung Guest   Posts: n/a This problem was addressed by Poinsot and Candel for the inviscid Burgers-Equation in Journal of Computational Physics, vol. 62, 282-296, 1986.

 February 12, 2001, 13:21 Re: Stability for Nonlinear Numerical Scheme #4 clifford bradford Guest   Posts: n/a 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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