Computational Methods in Physics : Compendium for Students / by Simon Širca, Martin Horvat.

Format:

Book

Author/Creator:

Širca, Simon.

Contributor:

Horvat, Martin.

Series:

Graduate Texts in Physics, 1868-4521

Language:

English

Subjects (All):

Mathematical physics.

Chemistry, Physical and theoretical.

Engineering mathematics.

Engineering--Data processing.

Engineering.

Mathematics--Data processing.

Mathematics.

Theoretical, Mathematical and Computational Physics.

Theoretical Chemistry.

Mathematical and Computational Engineering Applications.

Computational Science and Engineering.

Local Subjects:

Theoretical, Mathematical and Computational Physics.

Theoretical Chemistry.

Mathematical and Computational Engineering Applications.

Computational Science and Engineering.

Physical Description:

1 online resource (1815 pages)

Edition:

3rd ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This textbook provides a compendium of numerical methods to assist physics students and researchers in their daily work. It carefully considers error estimates, stability and convergence issues, the choice of optimal methods, and techniques to increase program execution speeds. The book supplies numerous examples throughout the chapters that are concluded by more comprehensive problems with a strong physics background. Instead of uncritically employing modern black-box tools, the readers are encouraged to develop a more ponderous and skeptical approach. This revised and expanded edition now includes a new chapter on numerical integration and stable differentiation, as well as fresh material on optimal filtering, integration of gravitational many-body problems, computation of Poincaré maps, regularization of orbits, singular Sturm-Liouville problems, techniques for time evolution and spatial treatment of (semi)infinite domains in spectral methods, and phase retrieval. It also brings updated discussions of algebraic problems involving sparse matrices and of high-resolution schemes for partial differential equations.

Contents:

Basics of Numerical Analysis

Solving Non-linear Equations

Numerical Integration and Differentiation

Matrix Methods

Transformations of Functions and Signals

Statistical Analysis and Modeling of Data

Modeling and Analysis of Time Series

Initial-value Problems for ODE

Boundary-value Problems for ODE

Difference Methods for One-dimensional PDE

Difference Methods for PDE in Two or more Dimensions

Spectral Methods for ODE and PDE

Inverse and Ill-posed Problems.

ISBN:

9783031685668

3031685660