Foundations of Computational Mathematics (London Mathematical Society Lecture Note Series)

Foundations of Computational Mathematics (London Mathematical Society Lecture Note Series) Review

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Foundations of Computational Mathematics (London Mathematical Society Lecture Note Series) Feature

The Society for the Foundations of Computational Mathematics supports fundamental research in a wide spectrum of computational mathematics and its application areas. As part of its endeavour to promote research in computational mathematics, the society regularly organizes conferences and workshops which bring together leading researchers in the diverse fields impinging on all aspects of computation. This book presents thirteen papers written by plenary speakers from the 1999 conference, all of whom are the foremost figures in their respective fields. Topics covered include complexity theory, approximation theory, optimization, computational geometry, stochastic systems and the computation of partial differential equations.

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Bioinformatics and Computational Biology Solutions Using R and Bioconductor (Statistics for Biology and Health)

Bioinformatics and Computational Biology Solutions Using R and Bioconductor (Statistics for Biology and Health) Review

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Bioinformatics and Computational Biology Solutions Using R and Bioconductor (Statistics for Biology and Health) Feature

Full four-color book.

Some of the editors created the Bioconductor project and Robert Gentleman is one of the two originators of R.

All methods are illustrated with publicly available data, and a major section of the book is devoted to fully worked case studies.

Code underlying all of the computations that are shown is made available on a companion website, and readers can reproduce every number, figure, and table on their own computers.

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Verification of Computer Codes in Computational Science and Engineering

Verification of Computer Codes in Computational Science and Engineering Review

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Verification of Computer Codes in Computational Science and Engineering Feature

How can one be assured that computer codes that solve differential equations are correct? Standard practice using benchmark testing no longer provides full coverage because today's production codes solve more complex equations using more powerful algorithms. By verifying the order-of-accuracy of the numerical algorithm implemented in the code, one can detect most any coding mistake that would prevent correct solutions from being computed.

Verification of Computer Codes in Computational Science and Engineering sets forth a powerful alternative called OVMSP: Order-Verification via the Manufactured Solution Procedure. This procedure has two primary components: using the Method of Manufactured Exact Solutions to create analytic solutions to the fully-general differential equations solved by the code and using grid convergence studies to confirm the order-of-accuracy. The authors present a step-by-step procedural guide to OVMSP implementation and demonstrate its effectiveness.

Properly implemented, OVMSP offers an exciting opportunity to identify virtually all coding 'bugs' that prevent correct solution of the governing partial differential equations. Verification of Computer Codes in Computational Science and Engineering shows you how this can be done. The treatment is clear, concise, and suitable both for developers of production quality simulation software and as a reference for computational science and engineering professionals.

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