# stability and nonlinear equation.

 Register Blogs Members List Search Today's Posts Mark Forums Read February 28, 2004, 10:56 stability and nonlinear equation. #1 bnedse Guest   Posts: n/a Hello, I want to know how I can check the stability of nonlinear system of equation. For example, if I have the following where everything is partial derivative: du_dt + f(u) du_dx = 0 then, how can I use Neumann stability analysis to analyize a particular discretization of this equation. Any help or references to textbook type information would be most kind.  February 28, 2004, 11:26 Re: stability and nonlinear equation. #2 rvndr Guest   Posts: n/a Linearity of the equation is a general requirement for the application of the von neumann stability analysis. But in this case your equation is non-linear so , locally linearize the non-linear equation and subsequently apply the von Neumann stability analysis. I hope this will help. rvndr  February 29, 2004, 18:37 Re: stability and nonlinear equation. #3 bnedse Guest   Posts: n/a O.k. Thank you for the help. How would you suggest I locally linearise it? Also, how can I show that if the equation is locally lineraised, that it reflects the non-linear version well? In other words, how do I see if linearising it destroys any relation to the orgiinal non linear equation.  March 2, 2004, 12:23 Re: stability and nonlinear equation. #4 Jane Hosky Guest   Posts: n/a when dealing with linear equations you often only need to examine the behaviour of a single component, as all other will behanve similarly. linearisation of your equation depends on the function of u, i.e. 1D linearlised Burgers equation: du_dt + c du_dx = 0 where c is constant and positive. this is a hyperbolic equation and leads to the CFL condition. if you assume an explicit scheme in your original equation: du_dt + f(u) du_dx = 0 linearisation is trivial, by assuming old values. for an implicit scheme a linearisation method is needed, or alternatively an iteration within a time step can be used. look at the work by beam and warming where it is suggested to expand the flux function using a taylor series. hope this helps Thread Tools Search this Thread Show Printable Version Email this Page Search this Thread: Advanced Search Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are On Refbacks are On Forum Rules Similar Threads Thread Thread Starter Forum Replies Last Post Runge_Kutta Main CFD Forum 33 September 9, 2019 16:32 JackMM Main CFD Forum 6 October 5, 2007 07:20 Bobby Main CFD Forum 10 August 5, 2005 15:43 Maciej Matyka Main CFD Forum 0 February 20, 2003 11:41 Guo Main CFD Forum 3 February 12, 2001 12:21

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