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Old   February 1, 2001, 13:34
Default Stability for Nonlinear Numerical Scheme
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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!
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Old   February 6, 2001, 10:59
Default Re: Stability for Nonlinear Numerical Scheme
Patrick Godon
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If you write the discretized non-linear equation assuming a first order perturbation


you can linearize the equation (after the discretization).

WOuld that help you ?

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Old   February 7, 2001, 12:51
Default Re: Stability for Nonlinear Numerical Scheme
Ralf Massjung
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This problem was addressed by Poinsot and Candel for the inviscid Burgers-Equation in Journal of Computational Physics, vol. 62, 282-296, 1986.
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Old   February 12, 2001, 13:21
Default Re: Stability for Nonlinear Numerical Scheme
clifford bradford
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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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