Models Methods Software

Dan Hughes

More on ODEs, MMS and Ill-Posed IVPs

First for the nomenclature: ODEs means Ordinary Differential Equations, MMS means the Method of Manufactured Solutions, and IVPs means Initial Value Problems.

This previous post provided some information on these subjects. So far as I know, that post presented the first results for application of MMS to ill-posed IVPs. That post suggested that for the numerical solution methods used therein, the original Lorenz system of 1963 has yet to be correctly solved.

I have some additional results, a summary of which is:
I think the Lorenz system has not yet been accurately integrated by any numerical solution methods. Higher-order methods plus, at the same time, higher precision representation of numbers will give results that might appear to be solutions. But, calculations for sufficiently long time spans will show that errors always increase.

I’ve uploaded a file here.

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October 8, 2010 Posted by | Verification | , , , , , | 3 Comments

Physical Realizations of Oxymoron

A Climate Scientist pleads for ( understanding / belief / sympathy / faith / acceptance ) and taking politics out of science by writing an Editorial Opinion column about politics, and while stating:

“Overloading the atmosphere with carbon dioxide from burning fossil fuels is heating the planet, shrinking the Arctic ice cap, melting glaciers and raising sea levels. It is leading to more widespread drought, more frequent heat waves and more powerful hurricanes. [ My bold ]

A two-fer; injecting politics into science and making statements not supported by science.

October 8, 2010 Posted by | Uncategorized | | Leave a comment