Highly recommended by CHOICE, previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB(R) Approach, Third Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computer results so that the main steps are easily visualized and interpreted. New to the Third Edition A chapter on the numerical solution of integral equations A section on nonlinear partial differential equations (PDEs) in the last chapter Inclusion of MATLAB GUIs throughout the text The book begins with simple theoretical and computational topics, including computer floating point arithmetic, errors, interval arithmetic, and the root of equations. After presenting direct and iterative methods for solving systems of linear equations, the authors discuss interpolation, spline functions, concepts of least-squares data fitting, and numerical optimization.
They then focus on numerical differentiation and efficient integration techniques as well as a variety of numerical techniques for solving linear integral equations, ordinary differential equations, and boundary-value problems. The book concludes with numerical techniques for computing the eigenvalues and eigenvectors of a matrix and for solving PDEs. CD-ROM Resource The accompanying CD-ROM contains simple MATLAB functions that help students understand how the methods work. These functions provide a clear, step-by-step explanation of the mechanism behind the algorithm of each numerical method and guide students through the calculations necessary to understand the algorithm. Written in an easy-to-follow, simple style, this text improves students' ability to master the theoretical and practical elements of the methods. Through this book, they will be able to solve many numerical problems using MATLAB.
Table of Contents:
Introduction
About MATLAB and MATLAB graphical user interface (GUI)
An introduction to MATLAB
Taylor series
Number System and Errors
Floating-point arithmetic
Round-off errors
Truncation error
Interval arithmetic
Roots of Equations
The bisection method
The method of false position
Fixed-point iteration
The secant method
Newton’s method
Convergence of the Newton and Secant methods
Multiple roots and the modified Newton method
Newton’s method for nonlinear systems
Applied problems
System of Linear Equations
Matrices and matrix operations
Naïve Gaussian elimination
Gaussian elimination with scaled partial pivoting
Lu decomposition
Iterative methods
Applied problems
Interpolation
Polynomial interpolation theory
Newton’s divided-difference interpolating polynomial
The error of the interpolating polynomial
Lagrange interpolating polynomial
Applied problems
Interpolation with Spline Functions
Piecewise linear interpolation
Quadratic spline
Natural cubic splines
Applied problems
The Method of Least Squares
Linear least squares
Least-squares polynomial
Nonlinear least squares
Trigonometric least-squares polynomial
Applied problems
Numerical Optimization
Analysis of single-variable functions
Line search methods
Minimization using derivatives
Applied problems
Numerical Differentiation
Numerical differentiation
Richardson’s formula
Applied problems
Numerical Integration
Trapezoidal rule
Simpson’s rule
Romberg algorithm
Gaussian quadrature
Applied problems
Numerical Methods for Linear Integral Equations
Introduction
Quadrature rules
The successive approximation method
Schmidt’s method
Volterra-type integral equations
Applied problems
Numerical Methods for Differential Equations
Euler’s Method
Error Analysis
Higher-order Taylor series methods
Runge-Kutta methods
Adams-Bashforth methods
Predictor-corrector methods
Adams-Moulton methods
Numerical stability
Higher-order equations and systems of differential equations
Implicit methods and stiff systems
Phase plane analysis: chaotic differential equations
Applied problems
Boundary-Value Problems
Finite-difference methods
Shooting methods
Applied problems
Eigenvalues and Eigenvectors
Basic theory
The power method
The quadratic method
Eigenvalues for boundary-value problems
Bifurcations in differential equations
Applied problems
Partial Differential Equations
Parabolic equations
Hyperbolic equations
Elliptic equations
Nonlinear partial differential equations
Introduction to finite-element method
Applied problems
Bibliography and References
Appendix A: Calculus Review
Appendix B: MATLAB Built-in Functions
Appendix C: Text MATLAB Functions
Appendix D: MATLAB GUI
Answers to Selected Exercises
Index
About the Author :
Abdelwahab Kharab is an associate professor in the College of Arts and Sciences at Abu Dhabi University. His research interests include numerical analysis and simulation for the numerical solution of partial differential equations that arise in science and engineering. Ronald B. Guenther is an Emeritus Professor in the Department of Mathematics at Oregon State University. His research interests include mathematically modeling deterministic systems and the ordinary and partial differential equations that arise from these models.
Review :
Praise for Previous Editions Kharab and Guenther offer an attractive, clear, error-free, and well-written introduction to numerical methods ! Highly recommended. --J.H. Ellison, CHOICE
