State the mathematical problem, e.g., "we want to compute an approximation to ...", and state in brief words the name of the numerical method used, e.g., "... using finite differences" (without stating formulas).
Explain your numerical method in detail, with suitable formulas; you might be able to just quote a proper page of the textbook, etc. This can be short if the algorithm is stated fully somewhere, but this section may be a major part of your report, if you have to collect a lot of information from various sources or have to derive all equations yourself! Then you should discuss the algorithm a little, e.g., say why you chose it, what theorems apply, what convergence behavior you expect in which quantity, and why you believe this might work. Then describe the code you implemented and include a printout of it. Mention how you tested your code; often, it is a good idea to compute a small case by hand to check. Finally, remember to specify all choices of numerical parameters that matter in the following but do not change within the compuational experiments, e.g., machine epsilon or details of the hardware and software used.
Describe the computational experiments performed; that is, state exactly the values of all parameters and other values that have not been specified, yet. Example: "We compute the approximation for step sizes h = 1 / 2^n for n = 1, 2, ..., 15." Then, introduce your results by explaining how they are presented; you must explicitly refer to every figure or table here and introduce each function plotted or column in table. The point is to define what your labels in the figures and tables mean. Use formulas as necessary to define quantities clearly. (As you try to write this part, it turns often out that definitions of quantities are better introduced as part of Section 2 above, where you discuss what convergence to expect from them.) You should mention results concretely here as well, e.g., for an error plot, you might observe that "the absolute value of the error is never larger than ...".
While you introduced your results in the previous section as a matter of fact, it is in this section that you want to contrast them with applicable theorems or compare results from several cases with each other. Notice that this section is often very short, namely if you set things up well in Section 2 (theorems quoted and convergence expectation specified) and then plot or print out exactly these quantities in Section 3.
Provide the full citations of your references here. I suggest to use the form of "author (year)" as in "Atkinson (1989)" for your in-text references, because they are easier to manage than numbered references such as "". Only references are allowed here that you are actually referring to from the text of your report; this contrasts a bibliography that might list additional sources not explicitly used in the text.
For each problem, start with a page of text, that introduces the code, tables, figures, etc. on the following pages. Those results should appear in the same order as they are mentioned in the text. Assemble everything in the order, in which you want me to read it! To aid me in grading, please maintain the organization in parts (a), (b), etc., if given in the assignment. Keep all pages together that belong to one problem. The text of your report must be complete enough such that the reader can understand how results were obtained; I will not read code to find out what you did! Include your name in the comments of each of your functions; I will not accept code without your name. There should not be any hand-written interpretations on your printouts; those comments should be contained within your text that introduces and interprets the printed results.
I strongly urge you to hand-write your reports on the homework. Unless you are very experienced, using any typesetting system will likely limit you in your use of formulas and arrangement. However, your reports should have the style and arrangement, as if they were prepared for professional type-setting using, e.g., proper headers, displayed formulas, etc. Leave sufficient margins and other spaces for me to provide comments and feedback to you.
Preparing the report that documents what you did and analyzes the results is an integral part of the assignment, whether the assignment asks for it explicitly or not. Complete and correct computer results will never count more than half of the score for the problem. When grading the reports, I will be guided by the questions: "Based on the information given, could I reproduce your results?" and "Are all pertinent questions about the performance of the numerical method addressed?"