Von Neumann Stability Analysis of the FTCS Scheme | Lecture 70 | Numerical Methods for Engineers

[@utkansivrikaya577]

The best explanation I have ever seen on the Internet about the Von Neumann Stability condition. Thank you Sir ! Best Regards

[@NurafzaMatali]

Awesome. I'm interested to know a stability analysis of the finite difference scheme for solving the two-dimensional elliptic PDE.

[@jawaharfathima]

Great video. How do we estimate the stable timestep for a heat equation with a constant source term?

[@kovidasurampudi1411]

Very clear in understanding the concept.

[@NadiaMorroco]

How we find stability of 3D fractional diffusion equation and also convergence plz help

[@julienmans3359]

In the subtitles "ansatz" is spelled ''onsets"

[@LOKI123ification]

KZbin is a bit creepy, At the moment I'm writing/building a solver from scratch, and I did know the basic problem and today I got the suggestion from youtube :) . But thank you for your explanation. So easy to understand, that it seams obvious. Thank you

[@sabyasachimukherjee5908]

You are awesome. The way you explain everything is superb.

[@katzil1771]

Why is it called explicit (scheme) if you need the step before?

[@ProfJeffreyChasnov]

You can plug in the solution for the previous step to immediately get the next step. Implicit methods need to solve a matrix equation.

[@sashacurcic1719]

How would one apply this to RK2 and RK4 schemes?

[@aadiduggal1860]

pretty sure this is used for PDEs not ODEs

[@sashacurcic1719]

@@aadiduggal1860 You can use Runge Kutta's for PDEs or ODEs. I don't understand your point.

[@jonasschafer6794]

For xi = 1 or -1 we are at the boundary of stability. Is it desirable for some reason for xi to be a value closer to 0 or is any value | xi| < 1 "equally good"? Love your videos by the way, fantastic explanation!

[@Urururopa]

Very nicely explained!

[@mohammadghani1379]

Nice, by the way, Does Von Neumann stability still work for the STEADY STATE?

[@pipertripp]

After you choose the ansatz, it all makes sense, but where on Earth does that ansatz come from? Also, thanks for this video. The stability analysis was really cool and missing from my text, so this was a nice supplement.

[@yiwang3437]

the Ansatz there is a single Fourier mode.

[@its-silachi]

its fluctuation of error as function of x, expressed by a fourier series

[@Snow-tm9ic]

@@its-silachi This is an elliptic equation so it will have a bounded solution thus he could represent it in terms of fourier series. But if the equation is a wave equation (hyperbolic) then how to get this stability operator???

[@bhoopendragupta4782]

nicely explained

[@martinperu6207]

Thank.. Please could you explain MOL method?

[@ProfJeffreyChasnov]

MOL = Method of Lines. Discretize spatial variable and solve a large system of odes. Haha, explained.

[@alirezasoleimani2524]

Wunderbare Erklärung

[@zizizouzou4316]

Bonjour monsieur, s'il vous plaît aidez-moi à stabilité de Fourier

[@jacobspark1863]

Brilliant

[@zizizouzou4316]

Good morning sùr please help me in stabilite