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Unformatted text preview: COSC 1002/1902 Computational Science in C Practical 9 This practical session involves the numerical solution of difference equations. The exercises involve calculating loan amortisation, and investigating nonlinear models for the growth of a species with non-overlapping generations. Before you begin these exercises, you should review the material in lecture 9. Download the codes logistic map1.c and logistic map2.c from the unit web pages and compile and run the codes and check that you get the results described in the lecture. If you succeed with this then you are ready to begin the exercises. If not consult a tutor, who can provide assistance. The exercises are for students in both units except where indicated (1002 means that the question is just for students in COSC 1002, and 1902 means that the question is just for students in COSC 1902). Remember to have a tutor mark off checkpoints as you reach them. Exercises 1. In section 9.2 of the lecture notes it is shown that the amount P k remaining to be paid after k repayments of a loan obeys the difference equation P k +1 = (1 + i ) P k- S, (1) where S is the amount of each repayment, and i is the interest rate per repayment interval. The quantity A = P is the total amount of the loan. Consider a home loan of $500,000 with an interest rate of 7.5% per annum, repaid fortnightly (note that this corresponds to i = 0 . 075 / 26 , since there are 26 fortnights in a year)., since there are 26 fortnights in a year)....
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- Three '09