Computational Physics : An Introduction

In a rapidly evolving field such as computational physics, six years is an eternity. Even though many of the elementary techniques described here are of venerable age, their assembly into sophisticated combined methods and their intensive application to ever new problems is an ongoing and exciting process. After six years, a new the new vistas edition of this textbook must therefore take into account some of that have opened up recently. Apart from these additions and some didactic improvements, the general struc­ ture of the book holds good. The first three chapters are devoted to a thorough, if concise, treatment of the main ingredients from numerical mathematics: finite differences, linear algebra, and stochastics. This exercise will prove valuable when we proceed, in chapters 4 and 5, to combine these elementary tools into powerful instruments for the integration of differential equations. The final chapters are devoted to a number of applications in selected fields: statistical physics, quantum mechanics, and hydrodynamics. I will gradually augment this text by web-resident sample programs. These will be written in JAVA and will be accompanied by short explanations and references to this text. Thus it may prove worthwhile to pay an occasional visit to my web-site www.ap.univie.ac.at/users/Franz.Vesely/ to see if any new applets have sprung up. The Essential Point In Computational Physics Is Not The Use Of Machines, But The Systematic Application Of Numerical Techniques In Place Of, And In Addition To, Analytical Methods, In Order To Render Accessible To Computation As Large A Part Of Physical Reality As Possible. The Various Available Techniques, Disparate As They May Seem, Are Traced Back To Only Three Main Methodological Sources; Finite Difference Calculus, Linear Algebra, And Stochastics. Each Algorithm Is Carefully Introduced And Every Computational Tool Is Explained In Terms Of Fundamental Numerical Techniques. Examples From Statistical Mechanics, Quantum Mechanics, And Hydrodynamics Are Employed To Bridge The Gap Between Basic Methodology And Modern Research. This Second Edition Of Franz Vesely's Renowned Textbook Takes Into Account The New Vistas That Have Opened Up Recently In This Rapidly Evolving Field. Furthermore, Web-based Sample Programs Augment The Text. By Franz J. Vesely. Front Matter....Pages i-xvii Front Matter....Pages 1-5 Finite Differences....Pages 7-20 Linear Algebra....Pages 21-45 Stochastics....Pages 47-83 Front Matter....Pages 85-88 Ordinary Differential Equations....Pages 89-123 Partial Differential Equations....Pages 125-155 Front Matter....Pages 157-159 Simulation and Statistical Mechanics....Pages 161-194 Quantum Mechanical Simulation....Pages 195-214 Hydrodynamics....Pages 215-238 Back Matter....Pages 239-259