Here are the LaTeX file:homework1.tex and the PostScript file:homework1.ps

Math 228B Computational Assignment 1 Winter 1999

Due: Monday, January 25, 1999

Project Format

Please provide a typed report (e.g. in LaTeX) in the following format.

1.

A statement of the problem to be solved.

2.

Three graphs of the numerical solution at some fixed time T₀>0 that show

(a)

the exact solution at time t = 0 ,

(b)

the exact solution at time t = T₀ ,

(c)

and the approximate solution at time t = T₀ for , h / 2 and h / 4.

So each of the three graphs has four curves.

3.

Three tables showing the error in each of the , L¹ and L² norms on each grid; i.e., for , h / 2 and h / 4. So, for example, the error in the L² norm is given by

$$\vert\vert u_{e}-u\vert\vert _{2} = \big[ \sum^N_{j=1} \big((u_e)^n_j - u^n_j)^{2} \big]^{1/2} .$$ (1)

These tables should

(a)

be similar to Table 1 in the notes (although I prefer to have decrease as one goes down a column, rather than along a row) and

(b)

have sufficient data to deduce the convengence rate of the numerical method.

4.

A brief analysis explaining your results.

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