A student's guide to numerical methods

A student's guide to numerical methods
I. H. Hutchinson, I. H. Hutchi ...
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Last edited by MARC Bot
November 13, 2020 | History

A student's guide to numerical methods

This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introductory class, this compact textbook provides a thorough grounding in computational physics and engineering.

Publish Date
Language
English
Pages
207

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Book Details


Table of Contents

pt. I. Fitting functions to data. Exact fitting ; Approximate fitting ; Tomographic image reconstruction ; Efficiency and non - linearity
pt. II. Ordinary differential equations. Reduction to first order ; Numerical integration of initial - value problems ; Multidimensional stiff equations : implicit schemes ; Leap - frog schemes
pt. III. Two - point boundary conditions. Examples of two - point problems ; Shooting ; Direct solution ; Conservative differences, finite volumes
pt. IV. Partial differential equations. Examples of partial differential equations ; Classification of partial differential equations ; Finite - difference partial derivatives
pt. V. Diffusion. parabolic partial differential equations. Diffusion equations ; Time - advance choices and stability ; Implicit advancing matrix method ; Multiple space dimensions ; Estimating computational cost
pt. VI. Elliptic problems and iterative matrix solution. Elliptic equations and matrix inversion ; Convergence rate ; Successive over - relaxation ; Iteration and non - linear equations
pt. VII. Fluid dynamics and hyperbolic equations. The fluid momentum equation ; Hyperbolic equations ; Finite differences and stability
pt. VIII. Boltzmann's equation and its solution. The distribution function ; Conservation of particles in phase - space ; Solving the hyperbolic Boltzmann equation ; Collision term
pt. IX. Energy - resolved diffusive transport. Collisions of neutrons ; Reduction to multigroup diffusion equations ; Numerical representation of multigroup equations
pt. X. Atomistic and particle - in - cell simulation. Atomistic simulation ; Particle - in - cell codes
pt. XI. Monte Carlo techniques. Probability and statistics ; Computational random selection ; Flux integration and injection choice
pt. XII. Monte Carlo radiation transport. Transport and collisions ; Tracking, tallying, and statistical uncertainty
pt. XIII. Next steps. Finite - element methods ; Discrete Fourier analysis and spectral methods ; Sparse - matrix iterative Krylov solution ; Fluid evolution schemes
Appendix A. Summary of matrix algebra. Vector and matrix multiplication ; Determinants ; Inverses ; Eigenanalysis.

Edition Notes

Includes bibliographical references and index.

Classifications

Dewey Decimal Class
518
Library of Congress
QA39.3 .H92 2015, QA39.3.H92 2015

The Physical Object

Pagination
xiv, 207 pages
Number of pages
207

Edition Identifiers

Open Library
OL27186843M
ISBN 10
1107095670, 1107479509
ISBN 13
9781107095670, 9781107479500
LCCN
2014043961
OCLC/WorldCat
897632430

Work Identifiers

Work ID
OL20006755W

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History

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November 13, 2020 Edited by MARC Bot import existing book
October 10, 2020 Edited by ImportBot import existing book
August 4, 2020 Edited by ImportBot import existing book
August 4, 2020 Edited by ImportBot import existing book
July 19, 2019 Created by MARC Bot Imported from marc_openlibraries_sanfranciscopubliclibrary MARC record