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Computational Methods in Physics

Compendium for Students

  • Simon Širca
  • Martin Horvat

Part of the Graduate Texts in Physics book series (GTP)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Simon Širca, Martin Horvat
    Pages 1-61
  3. Simon Širca, Martin Horvat
    Pages 63-119
  4. Simon Širca, Martin Horvat
    Pages 121-186
  5. Simon Širca, Martin Horvat
    Pages 187-247
  6. Simon Širca, Martin Horvat
    Pages 249-324
  7. Simon Širca, Martin Horvat
    Pages 325-390
  8. Simon Širca, Martin Horvat
    Pages 391-462
  9. Simon Širca, Martin Horvat
    Pages 463-531
  10. Simon Širca, Martin Horvat
    Pages 533-585
  11. Simon Širca, Martin Horvat
    Pages 587-642
  12. Simon Širca, Martin Horvat
    Pages 643-690
  13. Simon Širca, Martin Horvat
    Pages 691-766
  14. Back Matter
    Pages 767-880

About this book

Introduction

This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools.

The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.


Keywords

Computational Algorithms Computational Physics Textbook Mathematical Methods in Physics Numerical Analysis Textbook Numerical Methods in Physics Compendium Polynomial Equations Scalar Equations Solution of Nonlinear Equations Vector Equations

Authors and affiliations

  • Simon Širca
    • 1
  • Martin Horvat
    • 2
  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-78619-3
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-78618-6
  • Online ISBN 978-3-319-78619-3
  • Series Print ISSN 1868-4513
  • Series Online ISSN 1868-4521
  • Buy this book on publisher's site