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.
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.
Americans are Fully Committed to Protecting the Environment
So long as it doesn’t make too much noise.
For me, this situation speaks volumes.
Google Ads
Where are those Google Ads coming from ? Or, more nearly correctly, from where are those Google Ads coming?
Update: Today, this morning, September 3, 2010, I’m not seeing any ???
Do-it-Yourself at RealClimate.Org
This post at realclimate.org is very strange. The phrase do-it-yourself is in the Title for the post and repeated once in the first sentence. Searches show that the phrase does not appear anywhere else in the post.
What a strange way to write about anything. The alleged subject does not appear in the discussion.
Internal Variability=Weather and Numerical Artifacts
This post is based on some notes related to verification and numerical artifacts that I made back in early July.
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V&V and SQA: Part 3, Verification
Verification Activities
The focus of verification is the actual coding of the software with objectives to determine: (1) that the coding corresponds to the equations given in the specification document, (2) the order of accuracy of the numerical methods, and (3) the order of convergence of the numerical methods. In general, the latter two objectives are purely mathematical and go to the heart of the coding of the solution methods. Several of the procedures that are used to pursue these objectives are given in the following discussions.
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V&V and SQA: Part 5, SQA
Software Quality Assurance Procedures
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V&V and SQA: Part 2, Requirements for Production-Grade Software
The requirements for release of software for production-grade applications include:
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V&V and SQA: Part 1, Definitions and Characterization
I’m going to post a series of short summaries of some of the central aspects of verification, validation ( V&V ) and software quality assurance ( SQA ) for production-grade computer software. These subjects have received significant investigations starting in the 1980s ( more or less ) and have reached maturation and have been successfully applied to a wide range of scientific and engineering software. I don’t intend to give a complete exposition of the subjects, the field is much too big.
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