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An efficient formula for an automatic integrator based on trapezoidal rule
In the previous post, we discussed why doubling the number of segments in the automatic integrator based on multiple-segment trapezoidal rule is more efficient than increasing the number of segments one at a time.But this advantage involves having to store the individual function values from previous calculations and then having to retrieve them properly. This drawback can be circumvented very efficiently as explained below. What you will see is that there is no need to store individual function values.
Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.
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