Practical Scientific Computing

ISBN-13: 9780857092250 / Angielski / Miękka / 2011 / 208 str.

A. Muhammad; Victor Zalizniak

Opis

Scientific computing is about developing mathematical models, numerical methods and computer implementations to study and solve real problems in science, engineering, business and even social sciences. Mathematical modelling requires deep understanding of classical numerical methods. This essential guide provides the reader with sufficient foundations in these areas to venture into more advanced texts.

The first section of the book presents numEclipse, an open source tool for numerical computing based on the notion of MATLAB(R). numEclipse is implemented as a plug-in for Eclipse, a leading integrated development environment for Java programming. The second section studies the classical methods of numerical analysis. Numerical algorithms and their implementations are presented using numEclipse.

Practical scientific computing is an invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses. It will also be a useful handbook for postgraduate researchers and professionals whose work involves scientific computing.

• An invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses
• Guides the reader through developing a deep understanding of classical numerical methods
• Features a comprehensive analysis of numEclipse including numerical algorithms and their implementations

Spis treści

Preface

Acknowledgements

Part I

Chapter 1: Introduction

1.1 Getting Started

1.2 Interpreter

1.3 Program

Chapter 2: Expressions

2.1 Matrix

2.2 Real Number

2.3 Complex Number

2.4 Boolean

2.5 String

2.6 Structure

2.7 Cell

2.8 Range Expression

2.9 Boolean Expression

2.10 Relational Expression

2.11 Numerical Expression

Chapter 3: Statements

3.1 Assignment Statement

3.2 Loop Statements

3.3 Conditional Statements

3.4 Continue and Break Statements

Chapter 4: Programming

4.1 Program

4.2 Function

4.3 Procedure

4.4 Java Programming

4.5 C Programming

Chapter 5: Architecture

5.1 Front-end

5.2 Back-end

5.3 User Interface

5.4 Gnuplot Interface

5.5 Execution Engine

Chapter 6: Plotting

6.1 Simple Function Plot (fplot)

6.2 Two-Dimensional Plots

6.3 Three-Dimensional Plots

Part II

Chapter 7: Solving Nonlinear Equations

7.1 Calculation of Roots with the use of Iterative Functions

7.2 Exercises

Chapter 8: Solving Systems of Linear Equations

8.1 Linear Algebra Background

8.2 Systems of Linear Equations

8.3 Types of Matrices that arise from Applications and Analysis

8.4 Error Sources

8.5 Condition Number

8.6 Direct Methods

8.7 Iterative Methods

8.8 Exercises

Chapter 9: Computational Eigenvalue Problems

9.1 Basic Facts concerning Eigenvalue Problems

9.2 Localization of Eigenvalues

9.3 Power Method

9.4 Inverse Iteration

9.5 Iteration with a Shift of Origin

9.6 The QR Method

9.7 Exercises

Chapter 10: Introduction to Finite Difference Schemes for Ordinary Differential Equations

10.1 Elementary Example of a Finite Difference Scheme

10.2 Approximation and Stability

10.3 Numerical Solution of Initial Value Problems

10.4 Numerical Solution of Boundary Value Problems

10.5 Error Estimation and Control

10.6 Exercises

Chapter 11: Interpolation and Approximation

11.1 Interpolation

11.2 Approximation of Functions and Data Representation

11.3 Exercises

Bibliography