(a) Describe how the weights for the order 4 closed Newton-Cotes quadrature formula could be found. Do NOT calculate the weights.
(b) What are composite quadrature rules and why are they preferred to using higher order quadrature rules?
(c) What are the main characteristics of a predictor-corrector method for solving an initial value problem.
(d) In general, there are 3 conditions for stopping an iterative algorithm, describe each of them, and give an example of each by considering the problem of finding a solution of f(x) = 0.
Topics explored in this solution include: weights for Newton-Cotes quadrature formulas, composite and higher order quadrature rules, predictor-corrector method for solving an initial value problem, and the conditions for stopping an iterative algorithm.