The Linear Shooting Method
Consider the boundary value problem
y'' = 4*(y-x)
0 <= t <= 1
y(0) = 0
y(1) = 2
This problem can be transformed into a set of 4 first order initial value problems
of the form (done in class)
u1' = u2
u2' = 4*u1 - 4*x
u3' = u4
u4' = 4*u3
u1(0) = u2(0) = u3(0) = 0 and u4(0) = 1
Let's solve this problem with Euler's Method;
A simple script that solves this problem
can be downloaded here .
It uses the functions
deriv.m and
exact.m .
Here are some Results:
h=0.1
h=0.01
