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Numerical Analysis
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This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.Abstract:
Introduction. Mathematical approximations have been used since ancient times to estimate solutions, but with the rise of digital computing the field of numerical analysis has become a discipline in its own right. Numerical analysts develop and study algorithms that provide approximate solutions to various types of numerical problems, and they analyze the accuracy, efficiency and robustness of these algorithms. As technology becomes ever more essential for the study of mathematics, learning algorithms that provide approximate solutions to mathematical problems and understanding the accuracy of such approximations becomes increasingly important. This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis.read more
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An interpolatory approximation of the matrix exponential based on Faber polynomials
Igor Moret,Paolo Novati +1 more
TL;DR: In this paper, a method for the approximation of the matrix exponential obtained by interpolation in zeros of Faber polynomials is introduced, which relates this computation to the solution of linear IVPs.
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Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential
TL;DR: The fine agreement between the results obtained by the two different methods shows the feasibility of application of the proposed technique to calculate rarefied gas flows over the whole range of the Knudsen number.
Terrain navigation for underwater vehicles
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A mathematical model of the dynamics of scrapie in a sheep flock.
TL;DR: Numerical analyses using this model demonstrate that a scrapie outbreak is likely to be of long duration (several decades), will lead to reduction of scrapie susceptible allele frequency (but not to zero), and has different dynamics in homozygous and heterozygous susceptible sheep, even if these genotypes are equally susceptible.
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Group theory and differential transform analysis of mixed convective heat and mass transfer from a horizontal surface with chemical reaction effects
TL;DR: In this article, a laminar mixed convection boundary-layer flow over a horizontal plate, with chemical reaction, is considered and the governing equations are expressed in nondimensional form.