# ODE solution

1. May 26, 2013

### squenshl

1. The problem statement, all variables and given/known data
Consider the following second order ODE
$$y'' + 2y' - y = e^{-x}, \quad y(0) = y'(0) = 1.$$ Convert this to a system of first order equations and use the pc33assisys MATLAB file to compute the solution for y(2).

2. Relevant equations

3. The attempt at a solution
The system of first order equations is
$$u_1' = u_2 \\ u_2' = e^{-x}-2u_2+u_1$$ with $$u_1(0) = u_2(0) = 1.$$
The solution for y(2) is y(2) = 3.27 to 2 d.p. But my pc33assisys file doesn't give me this. All the relevant files are attached to run the program. Can someone help figure out what is wrong with my code.

Thanks.

#### Attached Files:

File size:
871 bytes
Views:
53
• ###### Ass3Q2.m
File size:
70 bytes
Views:
52
2. May 26, 2013

### milesyoung

There's a matrix indexing error in pc33assi3sys.m in the Adams-Moulton integration loop. Whoever wrote it also forgot to initialize f(1,:) for the first multi-step.

I've attached a corrected version.

#### Attached Files:

• ###### pc33assi3sys_corrected.m
File size:
914 bytes
Views:
47
3. May 26, 2013

Cheers mate