Numerical Mathematics and Computing, 5th Ed. - List of Fortran90 Codes

Numerical Mathematics and Computing
Fifth Edition
Ward Cheney & David Kincaid
Sample Fortran90 Codes

In the following table, each line/entry contains the program file name, the page number where it can be found in the textbook, and a brief description. Click on the program name to display the source code, which can be downloaded.
Chapter 1: Introduction
first.f90 6-7 First programming experiment
pi.f90 8 Simple code to illustrate double precision
Chapter 2: Number Representation and Errors
oct.f90 49 Print in octal format
hex.f90 50 Print in hexadecimal format
numbers.f90 60-61 Print internal machine representation of various numbers
xsinx.f90 77-79 Example of carefully programming f(x) = x - sinx
Chapter 3: Locating Roots of Equations
bisection.f90 94-95 Bisection method
rec_bisection.f90 95-96 Recursive version of bisection method
newton.f90 106-107 Sample Newton method
secant.f90 127-128 Secant method
Chapter 4: Interpolation and Numerical Differentiation
coef.f90 152-155 Newton interpolation polynomial at equidistant pts
deriv.f90 185-186 Derivative by center differences/Richardson extrapolation
Chapter 5: Numerical Integration
sums.f90 200 Upper/lower sums experiment for an integral
trapezoid.f90 207 Trapezoid rule experiment for an integral
romberg.f90 223-224 Romberg arrays for three separate functions
Chapter 6: More on Numerical Integration
rec_simpson.f90 241 Adaptive scheme for Simpson's rule
Chapter 7: Systems of Linear Equations
ngauss.f90 270-271 Naive Gaussian elimination to solve linear systems
gauss.f90 285-287 Gaussian elimination with scaled partial pivoting
tri.f90 301-302 Solves tridiagonal systems
penta.f90 304 Solves pentadiagonal linear systems
Chapter 8: More on Systems of Linear Equations
Chapter 9: Approximation by Spline Functions
spline1.f90 385 Interpolates table using a first-degree spline function
spline3.f90 404-406 Natural cubic spline function at equidistant points
bspline2.f90 427-428 Interpolates table using a quadratic B-spline function
schoenberg.f90 430-431 Interpolates table using Schoenberg's process
Chapter 10: Ordinary Differential Equations
euler.f90 448-449 Euler's method for solving an ODE
taylor.f90 451 Taylor series method (order 4) for solving an ODE
rk4.f90 462-463 Runge-Kutta method (order 4) for solving an IVP
rk45.f90 472-473 Runge-Kutta-Fehlberg method for solving an IVP
rk45ad.f90 474 Adaptive Runge-Kutta-Fehlberg method
Chapter 11: Systems of Ordinary Differential Equations
taylorsys1.f90 489-490 Taylor series method (order 4) for systems of ODEs
taylorsys2.f90 491 Taylor series method (order 4) for systems of ODEs
rk4sys.f90 491-493,496 Runge-Kutta method (order 4) for systems of ODEs
amrk.f90 510-513 Adams-Moulton method for systems of ODEs
amrkad.f90 513 Adaptive Adams-Moulton method for systems of ODEs
Chapter 12: Smoothing of Data and the Method of Least Squares
Chapter 13: Monte Carlo Methods and Simulation
test_random.f90 562-563 Example to compute, store, and print random numbers
coarse_check.f90 564 Coarse check on the random-number generator
double_integral.f90 574-575 Volume of a complicated 3D region by Monte Carlo
volume_region.f90 575-576 Numerical value of integral over a 2D disk by Monte Carlo
cone.f90 576-577 Ice cream cone example
loaded_die.f90 581 Loaded die problem simulation
birthday.f90 583 Birthday problem simulation
needle.f90 584 Buffon's needle problem simulation
two_die.f90 585 Two dice problem simulation
shielding.f90 586-587 Neutron shielding problem simulation
Chapter 14: Boundary Value Problems for Ordinary Differential Equations
bvp1.f90 602-603 Boundary value problem solved by discretization technique
bvp2.f90 605-606 Boundary value problem solved by shooting method
Chapter 15: Partial Differential Equations
parabolic1.f90 618-619 Parabolic partial differential equation problem
parabolic2.f90 620-621 Parabolic PDE problem solved by Crank-Nicolson method
hyperbolic.f90 633-634 Hyperbolic PDE problem solved by discretization
seidel.f90 642-645 Elliptic PDE solved by discretization/ Gauss-Seidel method
Chapter 16: Minimization of Functions
Chapter 17: Linear Programming

Addditional programs can be found at the textbook's anonymous ftp site:

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  Last updated: 5/20/2003