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Fourth Computing Project \\
Math/CS 375, Spring 1994 \\
Professor Coutsias \\
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This project is due May 2. Plan your work
so that if your computer is down a short period, your project will not be late.

This project will count as part of your grade so you must work independently.
It is permissible to discuss the project with your instructor, fellow students,
and friends. However, the computer programs and report must be done only
by the student doing the project.

The project is to acquire from netlib, or some other source, routines for
computing cubic spline interpolants using the two boundary conditions:
\begin{description}
\item[(i.)] ``Not-a-knot'' condition. That is the cubics in the first two
(last two) intervals are the same.
\item[(ii.)] ``Natural'' condition - $S''=0$ at the endpoints.
\end{description}
Also obtain routines to evaluate the interpolant and its first derivative.  

Use your code to compute interpolants of the following functions:
\begin{description}
\item[(i.)] $\cos{(\pi x)} \cdot e^{-x} , \ \ 0 \leq x \leq 4.$
\item[(ii.)] $\frac {1}{1+x^{2}} , \ \ -5 \leq x \leq 5.$
\item[(iii.)] $\sqrt{x} , \ \ 0 \leq x \leq 2.$
\end{description}
Use 5, 9, and 17 equally spaced nodes for each case.
Evaluate each interpolant at 100 equally spaced points and plot the results.
Plot the functions interpolated and compare them. For each interpolant
compute the maximum absolute error over the 100 points. Also, compute the
error in the first derivative. Estimate the convergence rate of the spline
and its first derivative in the form $e \approx K h^p$, that is estimate
the exponent, $p$. Is the rate the same in
all cases?

At a minimum you should turn in hardcopies of
all plots, a list of the maximum errors and a discussion of the results. 
Email your programs directly to blong@carina as before. 

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