An Introduction to Numerical Methods - A MATLAB Approach

This repository contains the contents of the CD-ROM accompanying the book "An Introduction to Numerical Methods - A MATLAB Approach" (ISBN: 1-58488-281-6) by Abdelwahab Kharab and Ronald B. Guenther, and published by Chapman & Hall/CRC

Software Requirements

To operate the Introduction to Numerical Methods CD ROM, Microsoft Windows 95, 98, 2000, ME or NT 4.x, must be installed on the host computer. In addition, the user will also need Matlab 5 or higher installed.

Hardware Requirements

The recommended hardware requirements to operate the Introduction to Numerical Methods CD ROM are listed below.

• Pentium 1 processor or higher.
• 16 MB RAM.
• Hard drive with 15 MB of available disk space.
• CD-ROM drive (4x).
• SVGA monitor at 800 x 600, 256 colors.

CD ROM Contents

The CD-ROM contains the following MATLAB m-functions, first ordered alphabetically and then by topic:

Alphabetical

Function	M-file	Description	Page	Section
9.4	abash.m	Adams-Bashford of orders 2, 3, and 4	277	9.6
9.5	amoulton.m	Adams-Moulton method	286	9.8
3.1	bisect.m	Bisection method	39	3.1
8.1	derive.m	Differentiation	211	8.1
9.1	euler.m	Euler's method	250	9.1
7.3	explsqr.m	Least squares fit, exponential	192	7.3
3.2	falsi.m	False position method	47	3.2
10.1	finitediff.m	Finite difference methods	315	10.1
3.5	fixed.m	Fixed point iteration	64	3.6
8.5	gauss_quad.m	Gaussian quadrature	242	8.4
4.2	gaussel.m	Gaussian elimination, scaled pivoting	96	4.3
12.1a	heat.m	Parabolic differential equations	364	12.1
12.1b	heat_crank.m	Parabolic differential equations	369	12.1
12.2	hyperbolic.m	Hyperbolic differential equations	377	12.2
7.4	hyplsqr.m	Least squares fit, hyperbolic	195	7.3
4.4	jacobi.m	Jacobi iteration	118	4.6
5.2	lagrange.m	Lagrange interpolation polynomial	149	5.4
12.3	laplace.m	Laplace's equation	385	12.3
7.1	linlsqr.m	Least squares fit, linear	179	7.1
10.2	lshoot.m	Linear shooting method	324	10.2
4.3	lufact.m	LU decomposition	106	4.4
9.2	midpoint.m	Midpoint method	266	9.4
3.4	newton.m	Newton's method	54	3.4
3.6	newton2.m	Newton's method, multiple roots	69	3.7
3.8	newton_sys.m	Newton's method for systems	76	3.8
5.1	newtondd.m	Interpolation, Newton differences	140	5.2
4.1	ngaussel.m	Gaussian elimination, naive	87	4.2
7.2	polylsqr.m	Least squares fit, polynomial	184	7.2
9.3	rk2_4.m	Runge-Kutta method, orders 2 and 4	267	9.4
8.4	romberg.m	Romberg integration	235	8.3
3.3	secant.m	Secant method	50	3.5
4.5	seidel.m	Gauss-Seidel iteration	121	4.7
8.3	simpson.m	Simpson's rule	226	8.2
6.1	spl1.m	Spline, linear	156	6.1
6.2	spl3.m	Spline, cubic	165	6.3
9.6	sys_rk4.m	System of differential equations	295	9.11
8.2	trapez.m	Trapezoidal rule	216	8.1

Topical

Roots of Equations

Function	M-file	Description	Page	Section
3.1	bisect.m	Bisection method	39	3.1
3.2	falsi.m	False position method	47	3.2
3.3	secant.m	Secant method	50	3.5
3.4	newton.m	Newton's method	54	3.4
3.5	fixed.m	Fixed point iteration	64	3.6
3.6	newton2.m	Newton's method, multiple roots	69	3.7
3.8	newton_sys.m	Newton's method for systems	76	3.8

System of Linear Equations

Function	M-file	Description	Page	Section
4.1	ngaussel.m	Gaussian elimination, naive	87	4.2
4.2	gaussel.m	Gaussian elimination, scaled pivoting	96	4.3
4.3	lufact.m	LU decomposition	106	4.4
4.4	jacobi.m	Jacobi iteration	118	4.6
4.5	seidel.m	Gauss-Seidel iteration	121	4.7

Interpolation

Function	M-file	Description	Page	Section
5.1	newtondd.m	Interpolation, Newton differences	140	5.2
5.2	lagrange.m	Lagrange interpolation polynomial	149	5.4

Interpolation with Spline Functions

Function	M-file	Description	Page	Section
6.1	spl1.m	Spline, linear	156	6.1
6.2	spl3.m	Spline, cubic	165	6.3

The Method of Least Squares

Function	M-file	Description	Page	Section
7.1	linlsqr.m	Least squares fit, linear	179	7.1
7.2	polylsqr.m	Least squares fit, polynomial	184	7.2
7.3	explsqr.m	Least squares fit, exponential	192	7.3
7.4	hyplsqr.m	Least squares fit, hyperbolic	195	7.3

Numerical Differentiation and Integration

Function	M-file	Description	Page	Section
8.1	derive.m	Differentiation	211	8.1
8.2	trapez.m	Trapezoidal rule	216	8.1
8.3	simpson.m	Simpson's rule	226	8.2
8.4	romberg.m	Romberg integration	235	8.3
8.5	gauss_quad.m	Gaussian quadrature	242	8.4

Numerical Methods for Ordinary Differential Equations

Function	M-file	Description	Page	Section
9.1	euler.m	Euler's method	250	9.1
9.2	midpoint.m	Midpoint method	266	9.4
9.3	rk2_4.m	Runge-Kutta method, orders 2 and 4	267	9.4
9.4	abash.m	Adams-Bashford of orders 2, 3, and 4	277	9.6
9.5	amoulton.m	Adams-Moulton method	286	9.8
9.6	sys_rk4.m	System of differential equations	295	9.11

Boundary-Value Problems

Function	M-file	Description	Page	Section
10.1	finitediff.m	Finite difference methods	315	10.1
10.2	lshoot.m	Linear shooting method	324	10.2

Partial Differential Equations

Function	M-file	Description	Page	Section
12.1a	heat.m	Parabolic differential equations	364	12.1
12.1b	heat_crank.m	Parabolic differential equations	369	12.1
12.2	hyperbolic.m	Hyperbolic differential equations	377	12.2
12.3	laplace.m	Laplace's equation	385	12.3

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