Got this problem and we've been given a program which can solve for x, for the equation:(adsbygoogle = window.adsbygoogle || []).push({});

Ax=b

Where

[tex]A = \left( \begin{array}{rrrrrr}

b & c & 0 & 0 & \cdots & 0 \\

a & b & c & 0 & \cdots & 0\\

0 & \ddots & \ddots & \ddots & & \vdots \\

\vdots & & \ddots & \ddots & \ddots & 0 \\

\vdots & & & \ddots & \ddots & c\\

0 & \cdots & \cdots & 0 & a & b \\

\end{array}

\right)[/tex]

If I left a = - 1, c = -1 and b = 2 + (1/n^2) (for my number of intervals n) and b = [1/n^2, 1/n^2, ..., 1/n^2]

Then I am approximation solutions to:

[tex]-\frac{d^2y}{dx^2} + y = 1 \quad \text{and} \quad y(0)=0 \quad y(1)=0[/tex]

I kind of understand that (or at least I have notes in front of me which seem to conclude that fairly logically). However I am now asked to set up a similar system for:

[tex]-\frac{d^2y}{dx^2} + 20 \frac{dy}{dx} = 1 \quad \text{and} \quad y(0)=0 \quad y(1)=0[/tex]

And I have no idea where to start, any help please.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Numerical solution of 2nd order ODE

**Physics Forums | Science Articles, Homework Help, Discussion**