Computational Methods for Physicists: Compendium for Students
This book helps 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 to the ways to optimize program execution speeds.
Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.
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Solving Nonlinear Equations
Transformations of Functions and Signals
Statistical Analysis and Modeling of Data
Modeling and Analysis of Time Series
InitialValue Problems for ODE
BoundaryValue Problems for ODE
Standard Numerical Data Types
Generation of Pseudorandom Numbers
Convergence Theorems for Iterative Methods
Fixed Points and Stability
Construction of Symplectic Integrators
Transforming PDE to Systems of ODE Two Warnings
Numerical Libraries Auxiliary Tools and Languages
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algorithm analysis approximation asymptotic basis functions boundary conditions boundary-value problems Chebyshev Chebyshev polynomials clusters coefficients collocation points components compute convergence correlation corresponding deﬁned denote dependence derivative difference scheme differential equations diffusion equation Dirichlet boundary conditions discrete discrete Fourier transform distribution eigenvalues eigenvectors elements error estimate Euler method example expansion explicit ﬁrst formula Fourier transform function f Gröbner bases high-resolution scheme Hilbert transform implicit initial condition initial-value problem integral interpolation interval inverse iteration Jacobi matrix LAPACK linear Math matrix mesh nodes non-linear numerical solution obtain orthogonal orthogonal polynomials oscillations Padé approximation parameter polynomials precision probability density quadrature random number random variable sample scalar Sect sequence shown in Fig SIAM signal solve space spectral Springer stability step symmetric tion values vector wavelet yn+1 zero