Answer: Many of the problems in this section call for fairly extensive numerical

Chapter 2, Problem 3

(choose chapter or problem)

Many of the problems in this section call for fairly extensive numerical computations. The amount of computing that it is reasonable for you to do depends strongly on the type of computing equipment that you have. A few steps of the requested calculations can be carried out on almost any pocket calculatoror even by hand if necessary. To do more, you will find at least a programmable calculator desirable, and for some problems a computer may be needed. Remember also that numerical results may vary somewhat depending on how your program is constructed and on how your computer executes arithmetic steps, rounds off, and so forth. Minor variations in the last decimal place may be due to such causes and do not necessarily indicate that something is amiss. Answers in the back of the book are recorded to six digits in most cases, although more digits were retained in the intermediate calculations. In each of 1 through 4: (a) Find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3, and 0.4 using the Euler method with h = 0.1. (b) Repeat part (a) with h = 0.05. Compare the results with those found in (a). (c) Repeat part (a) with h = 0.025. Compare the results with those found in (a) and (b). (d) Find the solution y = (t) of the given problem and evaluate (t) at t = 0.1, 0.2, 0.3, and 0.4. Compare these values with the results of (a), (b), and (c).