Various Consequences

About 6 months ago Dan Hughes sent me a link to an interesting paper on "chaotic" behavior in the trajectory of iterates in a num...

I quickly brushed over the method of manufactured solutions (MMS) aspects in the previous post on Lorenz 63 , you might wonder why. Well, it...

Dan Hughes has started an ambitious series of posts about formally verifying (using the method of manufactured solutions (MMS)) a range o...

Implicit Runge-Kutta methods are interesting because you can get high-order accuracy with relatively few stages. A method based on Radau qu...

I posted a while back on solving Burgers' equation on a moving grid . The same coordinate transformation techniques applied there can be...

I've been posting lately on solving Burgers' equation on moving grids , but haven't said much about difficulties involved in pro...

In the last post on solving Burgers' equation on a moving grid we ended up with the semi-discrete equation for the rates: where the spa...

Now that I've got a nice handy spectral derivative routine , time to test it out on some practical problems (ie non-smooth). A useful sc...