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.f | 6-7 | First programming experiment |
| pi.f | 8 | Simple code to illustrate double precision |
| Chapter 2: Number Representation and Errors | ||
| xsinx.f | 77-79 | Example of programming f(x) = x - sinx carefully |
| Chapter 3: Locating Roots of Equations | ||
| bisect1.f | 94-95 | Bisection method (versin 1) |
| bisect2.f | 95-96 | Bisection method (version 2) |
| newton.f | 106-107 | Sample Newton method |
| ` secant.f | 127 | Secant method |
| Chapter 4: Interpolation and Numerical Differentiation | ||
| coef.f | Newton interpolation polynomial at equidistant pts | |
| deriv.f | 185-186 | Derivative by center differences/Richardson extrapolation |
| Chapter 5: Numerical Integration | ||
| sums.f | 200 | Upper/lower sums experiment for an integral |
| trapezoid.f | 207 | Trapezoid rule experiment for an integral |
| romberg.f | 223-224 | Romberg arrays for three separate functions |
| Chapter 6: More on Numerical Integration | ||
| rec_simpson.f | 241 | Adaptive scheme for Simpson's rule |
| Chapter 7: Systems of Linear Equations | ||
| ngauss.f | 270-271 | Naive Gaussian elimination to solve linear systems |
| gauss.f | 285-287 | Gaussian elimination with scaled partial pivoting |
| tri_penta.f | 301,304 | Solves tridiagonal systems |
| Chapter 8: More on Systems of Linear Equations | ||
| Chapter 9: Approximation by Spline Functions | ||
| spline1.f | 385 | Interpolates table using a first-degree spline function |
| spline3.f | 404-406 | Natural cubic spline function at equidistant points |
| bspline2.f | 427-428 | Interpolates table using a quadratic B-spline function |
| schoenberg.f | 430-431 | Interpolates table using Schoenberg's process |
| Chapter 10: Ordinary Differential Equations | ||
| euler.f | 448-449 | Euler's method for solving an ODE |
| taylor.f | 451 | Taylor series method (order 4) for solving an ODE |
| rk4.f | 462-463 | Runge-Kutta method (order 4) for solving an IVP |
| rk45.f | 472-473 | Runge-Kutta-Fehlberg method for solving an IVP |
| rk45ad.f | 474 | Adaptive Runge-Kutta-Fehlberg method |
| Chapter 11: Systems of Ordinary Differential Equations | ||
| taylorsys.f | 489-491 | Taylor series method (order 4) for systems of ODEs |
| rk4sys.f | 491-493, 496 | Runge-Kutta method (order 4) for systems of ODEs |
| amrk.f | 510-513 | Adams-Moulton method for systems of ODEs |
| amrkad.f | 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.f | 562-563 | Example to compute, store, and print random numbers |
| coarse_check.f | 564 | Coarse check on the random-number generator |
| double_integral.f | 574-575 | Volume of a complicated 3D region by Monte Carlo |
| volume_region.f | 575-576 | Numerical value of integral over a 2D disk by Monte Carlo |
| cone.f | 576-577 | Ice cream cone example |
| loaded_die.f | 581 | Loaded die problem simulation |
| birthday.f | 583 | Birthday problem simulation |
| needle.f | 584 | Buffon's needle problem simulation |
| two_die.f | 585 | Two dice problem simulation |
| shielding.f | 586-587 | Neutron shielding problem simulation |
| Chapter 14: Boundary Value Problems for Ordinary Differential Equations | ||
| bvp1.f | 602-603 | Boundary value problem solved by discretization technique |
| bvp2.f | 605-606 | Boundary value problem solved by shooting method |
| Chapter 15: Partial Differential Equations | ||
| parabolic1.f | 618-619 | Parabolic partial differential equation problem |
| parabolic2.f | 620-621 | Parabolic PDE problem solved by Crank-Nicolson method |
| hyperbolic.f | 633-634 | Hyperbolic PDE problem solved by discretization |
| seidel.f | 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:
ftp://ftp.ma.utexas.edu/pub/cheney-kincaid/
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