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Numerical Analysis

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TLDR
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.

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Journal ArticleDOI

An interpolatory approximation of the matrix exponential based on Faber polynomials

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.
Journal ArticleDOI

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

TL;DR: In this thesis a terrain positioning method for underwater vehicles called the correlation method is presented and the well known problem with multiple terrain positions is discussed and the proposed method achieves this bound asymptotically.
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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.