Guidelines for numerical experiments

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Guidelines for numerical experiments

Always include your code and some runs of your program(s). You have to include enough information to convince me that your code is doing what is supposed to be doing. You will be penalized if you don’t, and it makes it harder for me to find potential mistakes.
Please present your numerical results in a way that highlights the intended results.
- For example if you are asked to compare several methods, you could do this with a plot of the actual vs computed values if their discrepancies are large enough. If the errors are too small, then plotting the error (or a table) is probably more meaningful.
- Keep in mind that semi-log or log-log scales (in Matlab: semilogy, semilogx, loglog ) often make it easier to interpret convergence curves.
- Your program output should include relevant information. For example if you have a method with adaptive time step, then it is good to know what the time step is at each iteration.
- The Matlab routine fprintf is very handy. It allows to use C style format strings for your program’s output. It works by first specifying what is to be printed and how. For floating point numbers there are 3 possible formats (in Matlab): %f (floating point as in 1.234 or 0.221), %e (exponent notation as in 1.234e+00 or 2.221e-01) or %g (which lets fprintf choose between %f and %e). One can also specify: the minimum number of characters to be printed and the number of digits after the period (the radix). For example %10.3f tells fprintf to format a floating point number as a float, using 10 characters and with 3 digits after the period. The line feed character is \n. Here is an example:
```
>> a=pi; b=pi/10000; c=pi*100000;
>> fprintf('%10.3f %10.3f %10.3f\n',a,b,c)
     3.142      0.000 314159.265
>> fprintf('%10.3g %10.3g %10.3g\n',a,b,c)
      3.14   0.000314   3.14e+05
>> fprintf('%10.3e %10.3e %10.3e\n',a,b,c)
 3.142e+00  3.142e-04  3.142e+05
>> fprintf('a=%10.3e, b=%10.3e c=%10.3e\n',a,b,c)
a= 3.142e+00, b= 3.142e-04 c= 3.142e+05
```
  See help fprintf or doc fprintf for more details.

I may present algorithms in a slightly different way than in the textbook. Unless specified, use the book’s algorithm because it will make it easier for you to test your code against the examples given in your book.

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