Numerical Methods for Calculus and
Differential Equations
MA 3457/CS 4033
B Term, 2009
M-Files
| Filename | Used
in
HW
# |
Description |
| census_demo.m | Demonstrates the behavior of interpolating polynomials on selected census data. | |
| cubic_spline_demo.m | Demonstrates the behavior of cubic splines on a set of design data. | |
| div_dif.m | 4 |
Computes Newton divided differences. |
| div_dif_hermite.m | 4 |
Computes divided differences for Hermite polynomial interpolation. |
| finite_difference_demo.m | 2 |
Demonstrates the behavior of forward- and central-difference derivative approximations on specified functions. |
| interp_demo.m | 4 |
Demonstrates the behavior of interpolating polynomials on selected functions and intervals. |
| mech_osc_demo.m | Demonstrates MATLAB's ode45, ode113, and ode15s on the mechanical oscillator initial-value problem. | |
| mech_osc_fun.m | Evaluates the right-hand side of the mechanical oscillator ODE; called by mech_osc_demo.m. | |
| ode45_examples.m |
Gives three examples of
ode45
usage. To use this, place the file in the directory in
which you are
using MATLAB, then type "edit ode45_examples.m" in the
MATLAB command
window. The file will appear in the editing window. It has
three
"cells" containing the examples. Click on the cell
corresponding to the
example you would like to run, then "evaluate" the cell
(i.e., run the
code in the cell). |
|
| pendulum_fun.m | Evaluates f(t,y) for the pendulum problem; called by unstable_soln_demo.m. | |
| p_eval.m | 4 |
Evaluates an interpolating polynomial in Newton form. |
| richardson.m | 7 |
Performs a specified number of steps of Richardson extrapolation. |
| romberg.m | 8 |
Performs a specified number of steps of Romberg integration. |
| runge_demo.m | Demonstrates
the
behavior of
interpolating polynomials on the Runge function. |
|
| runge_spline_demo.m | Demonstrates the behavior of cubic splines on the Runge function. | |
| stiff_demo_1.m | Implements the forward and backward Euler methods on the stiff ODE initial-value problem y' = -1000*(y-t^2) + 2*t, y(0) = 0; prints out the maximum error over [0,1]. | |
| stiff_demo_2.m | Implements the forward and backward Euler methods on the stiff ODE initial-value problem y' = -1000*(y-t^2) + 2*t, y(0) = 0; plots the maximum error over over [0,1] for a range of step values. | |
| unstable_soln_demo.m | Demonstrates the instability of the solution of the pendulum initial-value problem theta'' + sin(theta) = 0, theta(0) = 0, theta'(0) = 2. |