Programming Assignment Five


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\item{7a.}
Find a standard subroutine for solving tridiagonal systems 
of equations.
Use your mouse to connect to the National Institute of Standards
and Technology web page at{\tt\ http://math.nist.gov/}.
From this page select the following links in order:
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\itemitem{1.} Guide to Available Mathematical Software 
\itemitem{2.} What Problem it Solves
\itemitem{3.} Taxonomy as a Decision Tree
\itemitem{4.} D Linear Algebra
\itemitem{5.} D2 Solution of Systems of Linear Equations
\itemitem{6.} D2a Real Nonsymmetric Matrics
\itemitem{7.} D2a2 Banded
\itemitem{8.} D2a2a Tridiagonal
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How many routines solve the system
of linear equations $Ax=b$ where $A$ is a tridiagonal
matrix?  Download one of them and print it out.
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\item{7b.}
Consider the two-point linear boundary problem
$$
	\cases{
	y''+\cos(x)y'-(x^2+1)y=2\cr
	y(-2)=y(2)=-1.\cr
	}
$$
Find conditions on the grid size $h$
such that the corresponding central difference method is 
guaranteed to have a unique numerical solution.
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\item{7c.}
Use the central difference method to solve
the above boundary problem for grid sizes of $h=4/n$
where $n=4, 8, 16, 32, \ldots, 256$.
Plot your solutions.  Do they converge?
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\item{7d.}
Repeat for the homogeneous equation
$$
	\cases{
	y''+\cos(x)y'-(x^2+1)y=0\cr
	y(-2)=y(2)=-1.\cr
	}
$$
Do solutions to this equation have the weak min-max property?


Last Updated: Fri Nov 22 10:02:41 PST 2002