In many of the following problems, it will be essential to have a calculator or comp...

In many of the following problems, it will be essential to have a calculator or computer available. You may use a software package† or write a program for solving initial value problems using the improved Euler’s method algorithms on pages 127 and 128. (Remember, all trigonometric calculations are done in radians.)

Show that when the trapezoid scheme given in formula (8) is used to approximate the solution

for the constant e. Compute this approximation for h = 1, 10^-1, 10^-2, 10^-3, and 10^-4 and compare your results with those in Tables 3.4 and 3.5.