ENGLISH

A Student’s Guide to Numerical Methods

By Ian H. Hutchinson

Book information

ISBN
9781107095670, 9781107479500, 2014043961
Language
english
Format
PDF
Filesize
4 MB (4651664 bytes)
Pages
\260
Time added
2022-12-12 20:34:43

Description

Halftitle page Title page Dedication Copyright page Contents Preface 1 Fitting functions to data 1.1 Exact fitting 1.2 Approximate fitting 1.3 Tomographic image reconstruction 1.4 Efficiency and non-linearity 2 Ordinary differential equations 2.1 Reduction to first order 2.2 Numerical integration of initial-value problems 2.3 Multidimensional stiff equations: implicit schemes 2.4 Leap-Frog schemes 3 Two-point boundary conditions 3.1 Examples of two-point problems 3.2 Shooting 3.3 Direct solution 3.4 Conservative differences, finite volumes 4 Partial differential equations 4.1 Examples of partial differential equations 4.2 Classification of partial differential equations 4.3 Finite-difference partial derivatives 5 Diffusion. Parabolic partial differential equations 5.1 Diffusion equations 5.2 Time-advance choices and stability 5.3 Implicit advancing matrix method 5.4 Multiple space dimensions 5.5 Estimating computational cost 6 Elliptic problems and iterative matrix solution 6.1 Elliptic equations and matrix inversion 6.2 Convergence rate 6.3 Successive over-relaxation 6.4 Iteration and non-linear equations 7 Fluid dynamics and hyperbolic equations 7.1 The fluid momentum equation 7.2 Hyperbolic equations 7.3 Finite differences and stability 8 Boltzmann’s equation and its solution 8.1 The distribution function 8.2 Conservation of particles in phase-space 8.3 Solving the hyperbolic Boltzmann equation 8.4 Collision term 9 Energy-resolved diffusive transport 9.1 Collisions of neutrons 9.2 Reduction to multigroup diffusion equations 9.3 Numerical representation of multigroup equations 10 Atomistic and particle-in-cell simulation 10.1 Atomistic simulation 10.2 Particle-in-cell codes 11 Monte Carlo techniques 11.1 Probability and statistics 11.2 Computational random selection 11.3 Flux integration and injection choice 12 Monte Carlo radiation transport 12.1 Transport and collisions 12.2 Tracking, tallying, and statistical uncertainty 13 Next steps 13.1 Finite-element methods 13.2 Discrete Fourier analysis and spectral methods 13.3 Sparse-matrix iterative Krylov solution 13.4 Fluid evolution schemes Appendix A Summary of matrix algebra A.1 Vector and matrix multiplication A.2 Determinants A.3 Inverses A.4 Eigenanalysis References Index

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