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Comparison of Methods for Numerical Integration


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There are many methods for numerical integration. Most of these are of historical interest and only marginal practical value, because a very few stand far above the others. These are Gauss and Lobatto Quadrature. Gauss does not require the end points, while Lobatto does. Sometimes this makes a big difference. If you must integrate about a singular end point (like mc²=integral(mvdv/sqrt(1-v²/c²),v=0..c) use Gauss because v never gets to c. Of course, this particular integral has an analytical solution, but you can see how v=c results in a divide by zero. Some things reported in the literature are simply not true; for example, 5x5-point Gauss is nowhere near as accurate as 25-point Gauss, yet takes the same time to compute. You may also find inaccurate claims in the literature regarding the Romberg method, which is a pathetic waste compared to Gauss and one of the least efficient methods. I describe and compare every significant method for numerical integration in the attached paper. All of the source code is available in the attached zip file.

Comparison of Methods for Computing Cooling Tower Demand Curves.pdf NumericalIntegration.zip

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