The accuracy of any numerical method in solving a differential equation y′ = f(t, y) depen...

The accuracy of any numerical method in solving a differential equation y′ = f(t, y) depends on how strongly the equation depends on the variable y. More precisely, the constants that appear in the error bounds depend on the derivatives of f with respect to y. To see this experimentally, consider the two initial value problems

You will notice that the two problems have the same solution. For each of the three methods described in this chapter compute approximate solutions to these two initial value problems over the interval [0,1] using a step size of h = 0.01. For each method compare the accuracy of the solution to the two problems.