Ma 404: Numerical Methods
		     Reading and Homework Assignment 12
			     Prof. Wickerhauser


Read Chapter 9, Sections 9.4 to 9.9 of the text.

Do Algorithm 13 of Section 9.7, p.526.


Problem H12.1.  Write a computer program to solve the following initial value
problem on the interval [0,1]:

        y'(t) = 2*t*y(t), 0<t<1;     y(0)=1,

using the fourth-order Runge-Kutta method.  Have the program prompt the user
for the number of steps N, then use h=1/N as the step size.  Make a table of
the values y(1) for N=10, N=100, and N=1000.  Compare the results with the
exact value e=2.71828 18284 59045 23536 02874....



Problem H12.2.  Write a computer program to solve the initial value problem
of H12.1, using the Adams-Bashforth-Moulton predictor-corrector method.  Use
the fourth-order Runge-Kutta method to produce the initial values y_1, y_2,
y_3, f_1, f_2, and f_3.  Make a table of the values y(1) for N=10, N=100, and
N=1000 and compare the results with the exact value e.



Problem H12.3.  Write a computer program to solve the boundary value problem

    x''(t) = 2*t*x'(t)/(1+t*t) - 2*x(t)/(1+t*t) + 1;     x(0)=1, x(4)=-1,

over the interval [0,4].  Use shooting with any method (Euler, Runge-Kutta,
Heun, etc.) and a step size of 0.1 to compute a solution.



Problem H12.4.  Write a computer program to solve the boundary value problem
of Problem H13.3 using the finite difference method.  Choose h=0.1 and
compare the value at t=2 with the one given by the shooting method.