Lab 12 (1/11/2017)
In this lab, we will continue implementing ways of
solving ordinary differential equations. We shall
implement
Finite difference
and
Shooting methods for solving Boundary Value
Problems.
$$
\frac{d^2y}{dx^2} + f(x) = 0
$$
with two boundary conditions given by $y(0) = A, y(1) =
B$. Read Pages 48 - 51 of
Jeffrey
R. Chasnov.
Introduction to Numerical Methods for
details.
Problems
- Solve: $y^\prime(x) + 4y = 0, ~~~y(0) = -2,
y(\pi/4) = 10$. What happens if we change the
second boundary condition to $y(2\pi) = -2$?
- Use Shooting method to solve
$$ \frac{d^2y}{dx^2} + \frac{1}{x}\frac{dy}{dx} -
\frac{y}{x^2} = 0$$
with $y(5) = 0.003873, y(8) = 0.003070$.